Recent questions tagged ch3

If $ A=\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix},\;then\;A^5=?$

asked Jan 24, 2013 by meena.p

1 answer

If P and Q are equal matrices of same order such that PQ = QP, then prove by induction that $ PQ^n=Q^nP.$ Further, show that $(PQ)^n=P^n\times Q^n.$

asked Jan 24, 2013 by meena.p

0 answers

If $ A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$ find x and y such that $ A^2+xl=yA.\;Find\;A^{-1}.$

asked Jan 24, 2013 by meena.p

1 answer

Give that x = -9 is a root of $ \begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{vmatrix}=0$ find the other roots. Hint: Evaluate, find other roots.

asked Jan 24, 2013 by meena.p

0 answers

If $ \begin{bmatrix} \cos^2A & \cos A\sin A \\ \cos A\sin A & \sin^2A \end{bmatrix},Y=\begin{bmatrix} \cos^2B & \cos B\sin B \\ \cos B\sin B & \sin^2B \end{bmatrix}$then show that XY is a zero matrix, provided (A-B) is an odd multiple of $\large\pi/2$

asked Jan 24, 2013 by meena.p

0 answers

Prove that $\begin{bmatrix} (a+1) & (a+2) & (a+2) & 1 \\ (a+2) & (a+3) & (a+3) & 1 \\(a+3) & (a+4) & (a+4) & 1 \end{bmatrix}=-2$

asked Jan 24, 2013 by meena.p

0 answers

If $f(x)=3x^2-9x+7,$ then for a square matrix A, write f(A)

asked Jan 24, 2013 by meena.p

0 answers

Find a matrix X such that 2A + 2B + X = 0, where $ A = \begin{bmatrix} -1 & 3 \\ 2 & 1 \end{bmatrix} $ and $ B = \begin{bmatrix} 1 & 5 \\ 3 & 2 \end{bmatrix} $

asked Jan 24, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 4 & 1 \\ 5 & 8 \end{bmatrix},$ show that A + A' is symmetric matrix.

asked Jan 24, 2013 by thanvigandhi_1

1 answer

Find the matrix X such that :$ \begin{bmatrix} 2 & -1 \\ 0 & 1 \\ -2 & 4 \end{bmatrix}X=\begin{bmatrix} -1 & -8 & -10 \\ 3 & 4 & 0 \\10 & 20 & 10 \end{bmatrix}$

asked Jan 24, 2013 by meena.p

0 answers

The total number of elements in a matrix represents a prime number. How many possible orders a matrix can have.

asked Jan 24, 2013 by meena.p

0 answers

Prove the determinant $\begin{vmatrix} x & -\sin\alpha & \cos\alpha \\ \sin\alpha & -x & 1 \\ \cos\alpha & 1 & x \end{vmatrix}$ is independent as $\alpha$

asked Jan 24, 2013 by meena.p

0 answers

Prove that $ \begin{vmatrix} (b+c)^2 & ab & ca \\ ab & (a+c)^2 & bc \\ ca & bc & (a+b)^2 \end{vmatrix}=2abc(a+b+c)^2$ (Use properties to prove the above)

asked Jan 24, 2013 by meena.p

0 answers

Express $\begin{bmatrix} 2 & -3 \\ 1 & 4 \end{bmatrix}$ as sum of the symmetric and skew symmetric matrices.

asked Jan 24, 2013 by meena.p

0 answers

Using properties of Determinants prove that : $ \begin{vmatrix} a^2 & bc & ac+c^2 \\ a^2+ab & b^2 & ac \\ab & b^2+ac & c^2 \end{vmatrix}=4a^2b^2c^2$

asked Jan 24, 2013 by meena.p

0 answers

Prove that $\begin{vmatrix} x-3 & x-4 & x-a \\ x-2 & x-3 & x-b \\ x-1 & x-2 & x-c \end{vmatrix}=0,$ where a,b,c are in A.P

asked Jan 24, 2013 by meena.p

0 answers

Inverse of a square matrix is unique. Give an example to prove it?

asked Jan 24, 2013 by meena.p

0 answers

If $ A=\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}\;and\;A+A^T=1.$Find the possible values of $\theta=\large\pi/3.$

asked Jan 24, 2013 by meena.p

0 answers

If $ \begin{bmatrix} p & q \\ r & -p \end{bmatrix}$ is such that $A^2=1$ then find the value of $1-p^2+qr$

asked Jan 24, 2013 by meena.p

0 answers

If a+b+c=0 anb $ \begin{vmatrix} a-x & a & b \\ c & b-x & a \\ b & a & c-x \end{vmatrix}$ then prove that either x=0 or $x= \pm\sqrt{\frac{3}{2}(a^2+b^2+c^2)}$

asked Jan 24, 2013 by meena.p

0 answers

Find the value of a and b, if $\begin{bmatrix} 2 & -2 \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 2 & a \\ 3 & 2a+b \end{bmatrix} $

asked Jan 22, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix} $, then find x?

asked Jan 17, 2013 by thanvigandhi_1

1 answer

Using elementary transformation, find the inverse of the following matrix $ \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} $

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Evaluate [ 1 2 1 ] $ \begin{bmatrix} 2 \\ 4 \\ 2 \end{bmatrix}$

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Show that elements on the main diagonal of a skew-symmetric matrix are all zero.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Let $ \begin{bmatrix} 3 & y \\ x & 1 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 4 & 1 \end{bmatrix} $. Find the possible values of x and y, if x, y $ \in $ N.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} 3a-b & -2b \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 3 & 7 \end{bmatrix}$ then find a.

asked Jan 15, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$ and $ B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$, then find BA.

asked Jan 15, 2013 by thanvigandhi_1

1 answer

Show that the matrix $ A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix} $ is a skew - symmetric matrix.

asked Jan 11, 2013 by thanvigandhi_1

1 answer