Determinant

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

Click on each question to see answer & solution.

Question No: #21

Solve: $ \begin{vmatrix} 11-x & -6 & 2 \\ -6 & 10-x & -4 \\ 2 & -4 & 6-x \end{vmatrix} = 0 $
Ans: 3, 6, 18
SEE SOLUTION

Question No: #22

If $ A = \begin{bmatrix} 1 & -1 & 0 \\ 1 & 2 & -1 \\ 3 & 2 & -2 \end{bmatrix} $ then find the roots of `\det\ (A-xI_3)=0` where `I` is the unit matrix of order 3.

Question No: #23

If $ \begin{vmatrix} x-1 & 1 & 1 \\ 1 & x+1 & 1 \\ -1 & 1 & x+1 \end{vmatrix} =0 $, then show that values of `x` are `0, 1, -2`.

Question No: #24

Solve: $ \begin{vmatrix} x & a & b \\ a & x & b \\ a & b & x \end{vmatrix} = 0 $

Question No: #25

Solve : $ \begin{vmatrix} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{vmatrix} = 0 $

Question No: #26

Solve for `x`: $ \begin{vmatrix} x & c+x & b+x \\ c+x & x & a+x \\ b+x & a+x & x \end{vmatrix} = 0 $
Ans: `\frac{2abc}{a^2+b^2+c^2-2ab-2bc-2ca}`
SEE SOLUTION

Question No: #27

Solve: $ \begin{vmatrix} a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x \end{vmatrix} = 0 $
Ans: 0, 0, a
SEE SOLUTION

Question No: #28

Solve : $ \begin{vmatrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \end{vmatrix} = 0 $

Question No: #29

Solve: $ \begin{vmatrix} 1 & 3 & 9 \\ 1 & x & x^2 \\ 4 & 16 & 64 \end{vmatrix} = 0 $

Question No: #30

Solve. $ \begin{vmatrix} 15-2x & 11-3x & 7-x \\ 11 & 17 & 14 \\ 10 & 16 & 13 \end{vmatrix} = 0 $