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Recent questions tagged ch3
Questions
Find x if \( \begin{bmatrix} 3 & 4 \\ -5 & 2 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ -5 & 3 \end{bmatrix} \)
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Feb 3, 2013
by
thanvigandhi_1
1
answer
Find the value of x, if : $ \begin{bmatrix} 1 & x & 1 \end{bmatrix} \; \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 2 & 5 \end{bmatrix} \; \begin{bmatrix} 1 \\ -2 \\ 3 \end{bmatrix} = 0 $
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Feb 3, 2013
by
thanvigandhi_1
1
answer
Find the values of x, if $\begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q4
ch3
easy
math
asked
Feb 3, 2013
by
thanvigandhi_1
1
answer
If a matrix has 12 elements, what are the possible order it can have?
cbse
class12
modelpaper
2012
sec-a
q2
q2-1
ch3
easy
math
asked
Feb 2, 2013
by
thanvigandhi_1
1
answer
Find the product of matrix \( A = \begin{bmatrix} 3 \\ 2 \\ -5 \end{bmatrix} \) and its transpose.
cbse
class12
modelpaper
2012
sec-a
q4
ch3
easy
math
asked
Feb 2, 2013
by
thanvigandhi_1
1
answer
If $ A = \begin{bmatrix} 4 & 3 \\ 2 & 5 \end{bmatrix}$, find $x$ and $y$ such that $ A^2-xA+yI=0. $
cbse
class12
modelpaper
2012
sec-b
q12
ch3
medium
math
asked
Feb 2, 2013
by
thanvigandhi_1
1
answer
If \( A = \begin{bmatrix} cos\: \alpha & sin\: \alpha \\ -sin\: \alpha & cos\: \alpha \end{bmatrix} \), then show that AA' = I.
cbse
class12
modelpaper
2012
sec-a
q3
ch3
medium
math
asked
Jan 31, 2013
by
thanvigandhi_1
1
answer
Using elementary transformation, find the inverse of the matrix $\begin{bmatrix} 3 & 10 \\ 2 & 7 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-b
q13
ch3
medium
math
asked
Jan 30, 2013
by
thanvigandhi_1
1
answer
If \( A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta &\cos\theta \end{bmatrix} \) and $A + A'= I$, then find the value of \( \theta \).
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Jan 29, 2013
by
thanvigandhi_1
1
answer
If \( A = \begin{bmatrix} 2 & -2 \\ -3 & 4 \end{bmatrix} \), find \( -A^2+6A.\)
cbse
class12
modelpaper
2012
sec-a
q4
ch3
easy
math
asked
Jan 29, 2013
by
thanvigandhi_1
1
answer
If $ \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $, then find x.
cbse
class12
modelpaper
2012
sec-a
q5
ch3
easy
math
asked
Jan 29, 2013
by
thanvigandhi_1
1
answer
Find the values of x,y and z, if $ \begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Jan 28, 2013
by
thanvigandhi_1
1
answer
Express $ \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix} $ as the sum of a symmetic and skew-symmetric matrix.
cbse
class12
modelpaper
2012
sec-b
q13
ch3
easy
math
asked
Jan 28, 2013
by
thanvigandhi_1
1
answer
If \( A = \begin{bmatrix} 6 & -5 \\ 2 & 3 \end{bmatrix} \), then show that A-A' is skew matrix.
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Jan 27, 2013
by
thanvigandhi_1
1
answer
Find the value of x, such that \( A = \begin{bmatrix} x & 5 \\ 4 & 2x \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 16 & 4 \end{bmatrix} \)
cbse
class12
modelpaper
2012
sec-a
q10
ch3
easy
math
asked
Jan 27, 2013
by
thanvigandhi_1
1
answer
If \( A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{bmatrix} \), prove that $A^n = \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ \end{bmatrix} $, for \( n \in N.\)
cbse
class12
modelpaper
2012
sec-c
q23
ch3
medium
math
asked
Jan 27, 2013
by
thanvigandhi_1
1
answer
If A is a matrix of order 3 x 4 and B is matrix of order 5 x 4, what is the order of matrix (AB)'.
cbse
class12
modelpaper
2012
sec-a
q5
ch3
easy
math
asked
Jan 25, 2013
by
thanvigandhi_1
1
answer
If \( \begin{bmatrix} x+3 & 4 \\ y-4 & x+y \end{bmatrix} = \begin{bmatrix} 5 & 4 \\ 3 & 9 \end{bmatrix} \), find x and y.
cbse
class12
modelpaper
2012
sec-a
q4
ch3
easy
math
asked
Jan 25, 2013
by
thanvigandhi_1
1
answer
For any square matrix verify A(adj A) = |A|I
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q50
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} a & b \\ 0 & 1 \end{bmatrix}\;prove\;that\;A^n=\begin{bmatrix} \Large a^n & \Large\frac{b(a^n-1)}{a-1} \\ \normalsize 0 & 1 \end{bmatrix},n \epsilon N$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q49
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Let $\begin{vmatrix} 3 & y \\ x & 1 \end{vmatrix} =\begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix} $ find the possible values of x and y, find the values if x = y.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q48
p10
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If the points (2,0), (0,5) and (x,y) are collinear give a relation between x and y.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q47
p10
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If P and Q are invertible matrices of same order, then show that PQ is also invertible.
cbse
class12
kvquestionbank2012
ch3
q46
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find x, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} =0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q45
p10
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} \;find\;A^2\;Hence\;find\;A^6.$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q44
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $A=\begin{bmatrix} \cos \theta & \sin \theta & \\ -\sin \theta & \cos \theta \end{bmatrix} $ then show that $A^n=\begin{bmatrix} \cos 2\theta & \sin 2\theta & \\ -\sin 2\theta & \cos 2\theta \end{bmatrix} $
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q43
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If a, b, c are in A.P. then find the value of: $\begin{vmatrix} 2y+4 & 5y+7 & 8y+a \\ 3y+5 & 6y+8 & 9y+b \\ 4y+6 & 7y+9 & 10y+c \end{vmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q42
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If x, y and z all positive, are $p^{th},q^{th}and\;r^{th}$ terms of a G.P. Prove that $\begin{vmatrix} logx & p & 1 \\ logy & q & 1 \\ logz & r & 1 \end{vmatrix}=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q41
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find the quadratic function defined by the equation $ f(x)=ax^2+bx+c\;if\;f(0)=6,f(2)=11,f(-3)=6,$ using determinants.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q40
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A+B+C=\large\pi,\;\normalsize show\;that\;\begin{vmatrix} \sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0 \end{vmatrix}=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q39
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If x, y, z are positive and unequal show that the value of determinant $ \begin{vmatrix} x & y & z \\ y & z & x \\ z & x & y \end{vmatrix}$ is negative.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q38
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} 3 & -4 \\ -1 & 2 \end{bmatrix}$ find Matrix B such that AB= 1
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q37
p9
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If $A=\begin{bmatrix} \cos \theta & i\sin \theta \\ i\sin \theta & \cos \theta \end{bmatrix}$ then prove by Mathematical Induction that :$A^n=\begin{bmatrix} \cos n\theta & i\sin n\theta \\ i\sin n\theta & \cos n\theta \end{bmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q36
p9
math
sec-c
asked
Jan 24, 2013
by
meena.p
0
answers
If $ p(\alpha)=\begin{bmatrix} \cos \alpha & i\sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}\;show\;that\;p(\alpha) \times p(\beta)=p(\alpha+\beta)$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q35
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find the values of a and b such that $ A^2+aI=bA\;where\; A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q34
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} 1 & -2 & 1 \\ -2 & 3 & 1 \\ 1 & 1 & 5 \end{bmatrix}$ verify $(AdjA)^{-1}=adj(A^{-1})$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q33
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If two matrices $ A^{-1}\;and\;B$ are given how to find $(AB)^{-1}$verify with an example.\[(Find\; B^{-1} then\; find\; B^{-1} \times A^{-1})\]
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q32
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $P(a)=\begin{bmatrix} \cos a & -\sin a & 0 \\ \sin a & \cos a & 0 \\ 0 & 0 & 1 \end{bmatrix}$then show that $[P(x)]^{-1}=[P(-x)]$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q31
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find the matrix x if $ \begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix} \times \begin{bmatrix} 0 & 2 \\ 1 & 3 \end{bmatrix}=\begin{bmatrix} 1 & 6 \\ 3 & -2 \end{bmatrix}$\[X=-\frac{1}{4}\begin{bmatrix} -53 & 18 \\ 25 & -10 \end{bmatrix}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q30
p9
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If $A=\begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix} $satisfies the equation : $ x^2+6x+17=0\;find\;A^{-1}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q29
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $\begin{vmatrix} x & b & c \\ a & y & c \\ a & b & z \end{vmatrix}=0$ then find the value of $ \large\frac{x}{x-a}+\frac{y}{y-b}+\frac{z}{z-c}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q28
p8
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
Given $ A=\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$ such that $ |A|=-10.\;Find\;a_{11}c_{11}+a_{12}c_{12}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q27
p8
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If A is a non-singular matrix of order 3 and |A| = - 4 Find |adj A|
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q26
p8
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
For what value of 'K' the matrix $ \begin{bmatrix} k & 2 \\ 3 & 4 \end{bmatrix}$has no inverse.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q25
p8
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix},$ show that $ A^2-5A+7I=0,$ use the result to find $A^4$.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q24
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Let A and B be 3 x 3 matrices such that $ A^T=-A\;and\;B^T=B.$Then the matrix $\lambda(AB+3BA)$ is skew symmetric matrix for $\lambda$.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q23
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Assume X, Y, Z, W and P are matrices of order (2 x n), (3xk), (n x 3) and (p x k) respectively, then the restriction on n, k and p so that py + my will be defined are : (k=3, p=n)
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q22
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find the values of a, b, c if the matrix $\begin{bmatrix} 0 & 2b & c \\ a & b & -c \\ a & -b & c \end{bmatrix}$ satisfy the equation $ A^1A=I_3$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q21
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} 1& 1 & 1 \\ 1& 1 & 1 \\ 1& 1 & 1 \end{bmatrix}$ then prove that $ A^n=\begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix}\;n\in N$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q20
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If A and B are two matrices such that AB = B and BA = A then $A^2+B^2$=_______?_______\
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q19
p8
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
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