Matrix

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #31

If $ A = \begin{pmatrix} -1 & 5 \\ 3 & 2 \end{pmatrix} $ and $ B = \begin{pmatrix} 3 & -2 \\ 5 & 4 \end{pmatrix} $ then show that `(A+B)^T = A^T + B^T` and `(AB)^T = B^T\cdot A^T`

Question No: #32

If $ 2A - 3B = \begin{bmatrix} 1 & 4 \\ 2 & 8 \end{bmatrix} $ and $ 3A + 2B = \begin{bmatrix} -1 & 2 \\ 0 & 4 \end{bmatrix} $ , then find the matrix `A` and `B`.

Question No: #33

If $ A = \begin{bmatrix} \cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha \end{bmatrix} $ then prove that `A\cdotA^T = I`. Hence find `A^{-1]`

Question No: #34

Show that $ A = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & 1 \\ -1 & 1 \end{bmatrix} $ is a proper orthogonal matrix, and hence find `A^{-1}`.

Question No: #35

If $ \begin{pmatrix} x+y & 2 \\ 1 & 0 \end{pmatrix} = \begin{pmatrix} 2 & x-z \\ 2x-y & 0 \end{pmatrix} $ then find the value of `z`.
Ans: `-1`
SEE SOLUTION

Question No: #36

If $ 2 \begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix}$ then find the value of `x`, `y`

Question No: #37

If $ A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$ and $ kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$ then find the values of `k, a, b`.

Question No: #38

If the matrices `A` & `B`, given by $ A = \begin{bmatrix} x+y & y-z \\ 5-t & 7+x \end{bmatrix} $, $ B = \begin{bmatrix} t-x & z-t \\ z-y & x+z+t \end{bmatrix} $, are equal, then find the values of `x, y, z, t`
Ans: `x=1, y=2, z=3, t=4`
SEE SOLUTION

Question No: #39

If $ A = \begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix} $ and `A^2=I` then find the value of `x`.

Question No: #40

If $ A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix}$ and `A^2=kA-2I`, then find the value of `k`.