Matrix

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

Click on each question to see answer & solution.

Question No: #41

If $ A = \begin{pmatrix} 3 & 1 \\ 7 & 5 \end{pmatrix} $ and `A^2=-xI+yA` (where `I` is the identity matrix). Then find the value of `x` and `y`.

Question No: #42

If $ A = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix} $, $ B = \begin{bmatrix} a & 1 \\ b & -1 \end{bmatrix} $ and `(A+B)^2 = A^2+B^2`, then find the value of `a` and `b`.
Ans: `a=1, b=4`
SEE SOLUTION

Question No: #43

If $A=\begin{pmatrix} 2 & -1 \\ 3 & 2 \end{pmatrix}$ and $B=\begin{pmatrix} 0 & 4 \\ -1 & 7 \end{pmatrix}$ then find the matrix `3A^2-2B+I`

Question No: #44

If $ A = \begin{pmatrix} 4 & 2 \\ -1 & 1 \end{pmatrix} $ and $ I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} $ then prove that `(A-2I)(A-3I)=`$\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}$

Question No: #45

If $ A = \begin{bmatrix} 4 & 2i \\ i & 1 \end{bmatrix} $ then show that `(A-2I)(A-3I) = O` where `O` & `I` are zero & unit matrices. `i=\sqrt{-1}`

Question No: #46

If $ A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} $ and $ I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} $ , then prove that `A^2 - (a+d)A = (bc-ad)I`

Question No: #47

If $ A = \begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix} $ and $ B = \begin{bmatrix} 1 & 0 \\ 3 & 1 \end{bmatrix} $ and `A^2=B`, then find the value of `\alpha` (if possible). Give reason for your answer.

Question No: #48

If `\alpha` and `\beta` are two roots of the equation `x^2+x+1=0` then find the matrix `A` such that $ A = \begin{bmatrix} 1 & \beta \\ \alpha & \alpha \end{bmatrix} \times \begin{bmatrix} \alpha & \beta \\ 1 & \beta \end{bmatrix} $

Question No: #49

If $ \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 1 \\ -1 \end{pmatrix} $ then find the value of `x` and `y`.

Question No: #50

If $ A = \begin{bmatrix} 3 & -1 \\ 1 & 2 \end{bmatrix} $, $ B = \begin{bmatrix} 3 \\ 1 \end{bmatrix} $, $ C = \begin{bmatrix} 1 \\ -2 \end{bmatrix} $ and `AX=3B+2C`, then find the matrix `X`
Ans: $ X = \begin{bmatrix} 3 \\ -2 \end{bmatrix} $
SEE SOLUTION