Determinant

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

Click on each question to see answer & solution.

Question No: #1

If $ A = \begin{bmatrix} 11 & 20 \\ 31 & 41 \end{bmatrix} $ and `|3A|=k|A|`, then find the value of `k`, where `|A|` is determinant of matrix `A`.

Question No: #2

Let `A` be a square matrix of order `n\times\n`, and `k` is a scalar, then `|kA|` is equal to -- (a) `k|A|` (b) `nk|A|` (c) `n^k|A|` (d) `k^n|A|`

Question No: #3

Find co-factor of `-4` and `9` in determinant $ \begin{vmatrix} -1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9 \end{vmatrix} $

Question No: #4

If $ \begin{vmatrix} 6i & -3i & 1 \\ 4 & 3i & -i \\ 20 & 3 & i \end{vmatrix} = x+iy $, then find the values of `x` & `y` where `i=\sqrt{-1}`

Question No: #5

Value of the determinant $ \begin{vmatrix} 2^{10} & 2^{11} & 2^{12} \\ 2^{11} & 2^{12} & 2^{13} \\ 2^{12} & 2^{13} & 2^{14} \end{vmatrix} $ is -- (a) `2^10` (b) `0` (c) `1` (d) None of these.

Question No: #6

Find the value of $ \begin{vmatrix} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{vmatrix} $

Question No: #7

If `A` is a skew-symmetric matrix of odd order, then value of `|A|` is -- (a) `1` (b) `-1` (c) `0` (d) any real number.

Question No: #8

If `A` is an invertible matrix of order `2`, then the value of `\det(A^{-1})` is -- (a) `0` (b) `1` (c) `\det A` (d) `\frac{1}{\det A}`

Question No: #9

If $ A = \begin{bmatrix} x & 0 & 0 \\ 0 & x & 0 \\ 0 & 0 & x \end{bmatrix} $ then the value of `|A|\cdot|adj(A)|` is -- (a) `x^9` (b) `x^6` (c) `x^3` (d) `x`

Question No: #10

`A` be a `3\times\3` matrix. If `A^{-1}` exists and `|A|=6`, then the value of `|Adj(A)|` is -- (a) 1 (b) 6 (c) 12 (d) 36