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Recent questions tagged exemplar
Questions
True or False: Matrix multiplication is commutative.
cbse
class12
ch3
q87
p63
true-or-false
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: Matrix addition is associative as well as commutative.
cbse
class12
ch3
q86
p63
true-or-false
exemplar
toolbox
concepts
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: Matrices of different order can not be subtracted.
cbse
class12
ch3
q85
p63
true-or-false
exemplar
toolbox
concepts
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: Two matrices are equal if they have same number of rows and same number of columns.
cbse
class12
ch3
q84
p63
true-or-false
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: Matrices of any order can be added.
cbse
class12
ch3
q83
p63
true-or-false
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: A matrix denotes a number.
cbse
class12
ch3
q82
p63
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
In applying one or more row operations while finding $A^{-1}$ by elementary row operations, we obtain all zeros in one or more, then $A^{-1}$________ .
cbse
class12
ch3
q81
p63
fitb
exemplar
easy
sec-a
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ___________ .
cbse
class12
ch3
q80
p63
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A is symmetric matrix, then B'AB is ________ .
cbse
class12
ch3
q79
p63
fitb
exemplar
easy
sec-a
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A and B are symmetric matrices,then $\quad AB-BA\;is\;a\;\text{_______}$
cbse
class12
ch3
q78
q78-1
p63
fitb
exemplar
easy
sec-a
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A is skew symmetric, then kA is a __________. (k is any scalar).
cbse
class12
ch3
q77
p63
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A and B are square matrices of the same order,then $\quad (AB)'=\text{________}.$
cbse
class12
ch3
q76
q76-1
p63
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A is a skew symmetric matrix, then $A^2$ is a ____________ .
cbse
class12
ch3
q75
p62
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A is a symmetric matrix, then $A^3$ is a _________ matrix.
cbse
class12
ch3
q74
p62
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Matrix multiplication is __________ over addition.
cbse
class12
ch3
q73
p62
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
A matrix which is not a square matrix is called a __________ matrix.
cbse
class12
ch3
q72
p62
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
The product of any matrix by the scalar ____________ is the null matrix.
cbse
class12
ch3
q71
p62
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
The negative of a matrix is obtained by multiplying it by
cbse
class12
ch3
q70
p62
fitb
exemplar
math
sec-a
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Sum of two skew symmetric matrices is always ____________ matrix.
cbse
class12
ch3
q69
p62
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
________________ matrix is both symmetric and skew symmetric matrix.
cbse
class12
ch3
q68
p62
fitb
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
On using elementary row operations $R_2\times R_1-3R_2$ in the following matrix equation $\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$,we have:
cbse
class12
ch3
q67
p62
objective
exemplar
easy
sec-a
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
On using elementary column operations $C_2\times C_2-2C_1$ in the following matrix equation\[\begin{bmatrix}1 & 3\\2 & 4\end{bmatrix}=\begin{bmatrix}1 & 1\\0 & 1\end{bmatrix}\begin{bmatrix}3 & 1\\2 & 4\end{bmatrix}, \text{we have}\]
cbse
class12
ch3
q66
p61
objective
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
For any two matrices A and B,we have
cbse
class12
ch3
q65
p61
objective
exemplar
easy
sec-a
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A is a square matrix such that $A^2=I$,then $(A-I)^3+(A+I)^3-7A$ is equal to \[(A)\quad A\quad (B)\quad I-A\quad (C)\quad I +A\quad(D)\quad 3A\]
cbse
class12
ch3
q64
p61
objective
exemplar
math
sec-a
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A and B are matrices of same order ,then (AB'-BA') is a
cbse
class12
ch3
q63
p61
objective
exemplar
easy
sec-a
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If A is matrix of order $m\times n$ and B is a matrix such that AB' and B'A are both defined,then order of matrix B is
cbse
class12
ch3
q62
p61
objective
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
The matrix $\begin{bmatrix}0 & 5 & 8\\5 & 0 & 12\\8 & 12 & 0\end{bmatrix}$ is
cbse
class12
ch3
q61
p61
objective
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
The matrix $\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 4\end{bmatrix}$ is a
cbse
class12
ch3
q60
p60
objective
exemplar
sec-a
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If Matrix $A=[a_{ij}]_{2\times 3},$ where$a_{ij} \begin{array}{ 1 1}=1\;if\;i\neq j\\=0\;if\;i=j\end{array}$ then $\;A^2\;$ is equal to:
cbse
class12
ch3
q59
p60
objective
exemplar
easy
sec-a
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix},$then $A^2$ is equal to
cbse
class12
ch3
q58
p60
objective
exemplar
sec-a
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If A and B are two matrices of the order $3\times m\;and\;3\times n,$respectively,and m=n,then the order of matrix(5A-2B) is
cbse
class12
ch3
q57
p60
objective
exemplar
sec-a
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $\begin{bmatrix}2x + y & 4x\\5x - 7 & 4x\end{bmatrix}=\begin{bmatrix}7 & 7y - 13\\y & x + 6\end{bmatrix},$then the value of x,y is
cbse
class12
ch3
q55
p59
objective
exemplar
sec-a
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Total number of possible matrices of order $3\times 3$ with each entry 2 or 0 is
cbse
class12
ch3
q54
p59
objective
exemplar
math
sec-a
asked
Dec 23, 2012
by
sreemathi.v
1
answer
The matrix $P=\begin{bmatrix}0 & 0 & 4\\0 & 4 & 0\\4 & 0 & 0\end{bmatrix}$ is a
cbse
class12
ch3
q53
p59
objective
exemplar
sec-a
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Express the matrix $\begin{bmatrix}2 & 3 & 1\\1 & -1 & 2\\4 & 1 & 2\end{bmatrix}\;$as the sum of symmetric and skew symmetric matrices P&Q.
cbse
class12
ch3
q52
p59
exemplar
easy
sec-b
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If possible,using elementary row transformations,find the inverse of the following matrices $\quad\begin{bmatrix}2 & -1 & 3\\-5 & 3 & 1\\-3 & 2 & 3\end{bmatrix}$
cbse
class12
ch3
q51
q51-1
p59
exemplar
easy
sec-c
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find x,y,z if $A=\begin{bmatrix}0 & 2y & z\\x & y & -z\\x & -y & z\end{bmatrix}\;satisfies\;A'=A^{-1}$.
cbse
class12
ch3
q50
exemplar
sec-c
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If AB=BA for any two square matrices,prove by mathematical induction that $(AB)^n=A^nB^n$.
cbse
class12
ch3
q49
p58
exemplar
sec-c
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If A,B are square matrices of same order and B is a skew-symmetric matrix,show that A'BA is skew symmetric.
cbse
class12
ch3
q48
p58
short-answer
exemplar
easy
sec-b
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If A is square matrix such that $A^2=A,$show that $(I+A)^3=7A+I.$
cbse
class12
ch3
q47
p58
short-answer
sec-b
easy
exemplar
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $P(x)=\begin{bmatrix}\cos x & \sin x\\-\sin x & \cos x\end{bmatrix}$,then show that\[P(x).P(y)=P(x+y)=P(y).P(x).\]
cbse
class12
ch3
q46
p58
short-answer
easy
sec-b
exemplar
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find the value of $\alpha$ if $A=\begin{bmatrix}\cos\alpha & \sin\alpha\\-\sin\alpha & \cos\alpha\end{bmatrix}$ and $\;A^{-1}=A'$
cbse
class12
ch3
q44
p58
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If the matrix $\begin{bmatrix}0 & a & 3\\2 & b & -1\\c & 1 & 0\end{bmatrix}\;$is a skew symmetric matrix,find the values of a,b and c.
cbse
class12
ch3
q45
p58
short-answer
exemplar
sec-b
medium
qod
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2\\4 & 1\end{bmatrix},find\;A^2+2A+7I.$
cbse
class12
ch3
q43
p58
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find the matrix A such that$\begin{bmatrix}2 & -1\\1 & 0\\-3 & 4\end{bmatrix}\;A=\begin{bmatrix}-1 & -8 & -10\\1& -2 & -5\\9 & 22 &15\end{bmatrix}.$
cbse
class12
ch3
q42
p58
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find the values of a,b,c and d,if $3\begin{bmatrix}a & b\\c & d\end{bmatrix}=\begin{bmatrix}a & 6\\-1 & 2d\end{bmatrix}+\begin{bmatrix}4 & a+b\\c+d & 3\end{bmatrix}$
cbse
class12
ch3
q41
p58
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}3 & -5\\-4 & 2\end{bmatrix},$ then find $A^2-5A-14I.$Hence,obtain $A^3$.
cbse
class12
ch3
q40
p58
short-answer
exemplar
easy
sec-c
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 5\\7 & 12\end{bmatrix}\;and\;B=\begin{bmatrix}9 & 1\\7 & 8\end{bmatrix},$ find a matrix $C$ such that $3A+5B+2C$ is a null matrix.
cbse
class12
ch3
q39
p57
short-answer
exemplar
sec-a
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find inverse,by elementary row operations(if possible),of the following matrices$\quad\begin{bmatrix}1 & 3\\-5 & 7\end{bmatrix}$
cbse
class12
ch3
q37
q37-1
p57
short-answer
exemplar
sec-b
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Prove by Mathematical Induction that $(A')^n=(A^n)'$,where $n\in N$ for any square matrix A.
cbse
class12
ch3
q36
p57
short-answer
exemplar
sec-b
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
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