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CBSE XII
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Matrices
$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(iii)\quad(KA)'=(KA')$
cbse
class12
ch3
q27
q27-3
p56
short-answer
exemplar
sec-a
easy
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(ii)\quad(AB)'=B'A'$
cbse
class12
ch3
q27
q27-2
p56
short-answer
exemplar
easy
sec-b
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2\\-2 & 1\end{bmatrix},B=\begin{bmatrix}2 & 3\\3 & -4\end{bmatrix}\;and\;C=\begin{bmatrix}1 & 0\\-1 & 0\end{bmatrix},verify:(ii)\;A(B+C)=AB+AC$
cbse
class12
ch3
q22
q22-2
p55
shortanswer
exemplar
sec-b
medium
math
asked
Mar 5, 2013
by
sreemathi.v
1
answer
A manufacturer produces three products $( x, y, z )$ which he sells in two markets. Annual sales are indicated below: \[ \begin{array} { c c } \textbf{Market} & \textbf{Products} \\ I & 10,000 \quad 2,000 \quad 18,000 \\ II & 6,000 \quad 20,000 \quad 8,000 \end{array} \] If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.
cbse
class12
bookproblem
ch3
misc
q10
p101
easy
10-2
sec-b
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iv) \begin{bmatrix} 1 & 5 \\ -1 & 2 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec3
q10
p89
medium
sec-b
q10-4
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iii) \begin{bmatrix} 3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec3
q10
p89
medium
sec-b
q10-3
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $ (ii) \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec3
q10
p89
medium
sec-b
q10-2
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $(ii) (A - A') $ is a skew symmetric matrix.
cbse
class12
bookproblem
ch3
sec3
q8
p89
easy
sec-b
q8-1
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
$ (ii)$ Show that the matrix $ A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew symmetric matrix. $
cbse
class12
bookproblem
ch3
sec3
q7
p89
medium
sec-b
q7-2
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
$(ii) If A = \begin{bmatrix} sin\alpha & cos\alpha \\ -cos\alpha & sin\alpha \end{bmatrix}$ then verify that $A'A = I $
cbse
class12
bookproblem
ch3
sec3
q6
p89
easy
sec-b
q6-2
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (ii) } A = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix} \text{ , } B = \begin{bmatrix} 1 & 5 & 7 \end{bmatrix} $$
cbse
class12
bookproblem
ch3
sec3
q5
p88
easy
q5-2
sec-b
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix}$, then verify that $ (ii) ( A - B )' = A' - B' $
cbse
class12
bookproblem
ch3
sec3
q3
p88
easy
shortanswer
q3-2
sec-b
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
If $A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} $then verify that $ (ii) (A-B)' = A' - B'$
cbse
class12
bookproblem
ch3
sec3
q2
p88
easy
q2-2
sec-b
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
If $X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$ and $Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$, find a matrix $Z$ such that $X+Y+Z$ is a zero matrix.
cbse
class12
ch3
q7
q7-3
p53
shortanswer
exemplar
sec-a
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
If $X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$ and $Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$, find $2X-3Y$
cbse
class12
ch3
q7
q7-2
p53
short-answer
exemplar
sec-a
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
Construct $a_{2\times 2}$ matrix where $a_{ij} =|2i+3j|$
cbse
class12
ch3
q3
q3-2
p53
short-answer
exemplar
sec-a
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
In the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix}$, write the elements $a_{23}$, $a_{31}$, $a_{12}$
cbse
class12
ch3
q2
q2-3
p52
shortanswer
exemplar
sec-a
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
In the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix} write:(ii) Element\; of \;the\; matrices.$
cbse
class12
ch3
q2
q2-2
p52
shortanswer
exemplar
sec-a
easy
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
(iii) Find the transpose of the matrix \begin{bmatrix} -1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1 \end{bmatrix}
cbse
class12
bookproblem
ch3
sec3
q1
q1-3
p88
easy
sec-a
math
asked
Mar 1, 2013
by
sharmaaparna1
1
answer
Find the transpose of the following matrices: $ \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$
cbse
class12
bookproblem
ch3
sec3
q1
q1-2
p88
easy
sec-a
math
asked
Mar 1, 2013
by
balaji.thirumalai
1
answer
Find the transpose of each of the following matrices :$ (i) \begin{bmatrix} 5 \\ \tfrac{1}{2} \\ -1 \end{bmatrix}$
cbse
class12
bookproblem
ch3
q1-1
easy
p88
sec-a
shortanswer
math
asked
Mar 1, 2013
by
balaji.thirumalai
1
answer
A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5 $\%$ interest per year, and the second bond pays 7 $\%$ interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: b) Rs. 2000
cbse
class12
bookproblem
ch3
sec2
p82
medium
q19-2
shortanswer
sec-b
math
asked
Mar 1, 2013
by
balaji.thirumalai
1
answer
A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: a) Rs. 1800.
cbse
class12
bookproblem
ch3
p82
q18-1
easy
shortanswer
sec-b
math
asked
Mar 1, 2013
by
balaji.thirumalai
1
answer
Show that: $ii) \qquad \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p81
easy
q14
q14-2
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Show that: $(i) \qquad \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p81
easy
q14
q14-1
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Find $X$ and $Y$ if $(ii) \quad 2X + 3Y = \begin{bmatrix} 2 & 3 \\ 4 & 0 \end{bmatrix} \text{ and } 3X + 2Y = \begin{bmatrix} 2 & -2 \\ -1 & 5 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p81
medium
q7-2
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Find $X$ and $Y$ if: $(i) \quad X + Y = \begin{bmatrix} 7 & 0 \\ 2 & 5 \end{bmatrix} \text{ and } X - Y = \begin{bmatrix} 3 & 0 \\ 0 & 3 \end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p81
easy
q7-1
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(vi)\;\begin{bmatrix}3 & -1 &3\\-1 & 0 &2\end{bmatrix}\begin{bmatrix}2 & -3\\1 & 0\\3 & 1\end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-6
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(v)\;\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-5
shortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products:$ (iv)\;\begin{bmatrix}2 & 3 &4\\3 & 4 &4\\4 & 5 & 6\end{bmatrix}\begin{bmatrix}1 & -3 & 5\\0 & 2 &4\\3 & 0 & 5\end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-4
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(iii)\;\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-3
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(ii)\;\begin{bmatrix}1\\2\\3\end{bmatrix}\begin{bmatrix}2 & 3 & 4\end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-2
sec-b
shortanswer
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}\begin{bmatrix}a &-b\\b & a\end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-1
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the following $ (iv)\;\begin{bmatrix}\cos^2x & \sin^2x\\ \sin^2x & \cos^2x\end{bmatrix}+\begin{bmatrix}\sin^2x & \cos^2x\\ \cos^2x & \sin^2x\end{bmatrix}$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q2-4
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the following $ (iii)\;\begin{bmatrix}-1 & 4 & -6\\8 & 5 &16\\2 & 8 &5\end{bmatrix}+\begin{bmatrix}12 & 7 & 6\\8 & 0 & 5\\3 & 2 & 4\end{bmatrix}$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q2-3
shortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the following $(i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}+\begin{bmatrix}a & b\\b & a\end{bmatrix}$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q2-1
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ (v)\;BA\qquad$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-5
veryshort
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ AB\qquad$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-4
veryshort
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ 3A-C$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-3
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$ Find: $(ii) (A-B)\qquad$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-2
veryshortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $\;A+B\qquad$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-1
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Find the values of x,y and z from the following equations: $(iii)\;\begin{bmatrix}x+y+z\\x+z\\y+z\end{bmatrix}=\begin{bmatrix}9\\5\\7\end{bmatrix}$
class12
cbse
bookproblem
ch3
sec1
p64
easy
q6-3
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Find the values of x,y and z from the following equations:$ (ii)\;\begin{bmatrix}x+y & z\\5+z & xy\end{bmatrix}=\begin{bmatrix}6 & 2\\5 & 8\end{bmatrix}\qquad$
class12
cbse
bookproblem
ch3
sec1
p64
easy
q6-2
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Find the values of x,y and z from the following equations:$(i)\begin{bmatrix}4 & 3\\x & 5\end{bmatrix}=\begin{bmatrix}y & z\\1 & 5\end{bmatrix}\qquad$
class12
cbse
bookproblem
ch3
sec1
p64
easy
q6-1
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Construct a 3 x 4 matrix,whose elements are given by:$(i)\;a_{ij}=\frac{1}{2}| -3i+j\;| \qquad$
class12
cbse
bookproblem
ch3
sec1
p64
easy
q5-1
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Construct a 2 x 2 matrix, $A=[a_{ij}],$whose elements are given by:$ (ii) a_{ij}=\frac{i}{j}\qquad$
class12
cbse
bookproblem
ch3
sec1
p64
easy
q4-2
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Construct a $2 \times 2$ matrix, $A=[a_{ij}],$whose elements are given by: $a_{ij}=\frac{(i+j)^2}{2}\qquad$
class12
cbse
bookproblem
ch3
sec1
p64
easy
q4-1
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
If a matrix has 5 elements,what are the possible orders can it have?
class12
cbse
bookproblem
ch3
sec1
p64
easy
q3-1
veryshortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
If a matrix has 18 elements,what are the possible orders it can have?
class12
cbse
bookproblem
ch3
sec1
p64
easy
q3-1
veryshortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
If a matrix has 13 elements,what are the possible orders it can have? (Note: This question has been split into 2 questions)
class12
cbse
bookproblem
ch3
sec1
p64
easy
q2-2
veryshortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
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