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QUESTION: 1

If the value of the determinant , then the value of is

Solution:

Determinant = -2(-12 + 12) -2(-6 - 2) +1(-12 - 4)

= - 2(0) - 2(-8) + 1(16)

= 0 + 16 + 16

= 32

QUESTION: 2

The value of x, if = 0 , is

Solution:

QUESTION: 3

If the value of , then the value of

Solution:

If you interchange (switch) two rows (or columns) of a matrix A to get B, then det(B) = –det(A). Hence, the determinant is -(-7)

= 7

QUESTION: 4

The operation that will simplify the Determinant

by taking (a+b+c) common from the first Row is

Solution:

R_{1} ------> R_{1} + R_{2}, taking (a+b+c) common from the first row, we get the resultant matrix.

QUESTION: 5

The value of the determinant is

Solution:

|A|=3((4)-(4))-2((-4)-(2))-1((-8)-(-4))

|A|= -2(-6)-(-6)

|A|= -2(0)

=0

QUESTION: 6

The value of the Δ

Solution:

QUESTION: 7

If the value of the determinant is equal to 14, then the value of the determinant is equal to

Solution:

Taking 3 common from the column I in second determinant, we get the 14 * 3 = 42

QUESTION: 8

The value of is

Solution:

A = {(5x+2, 2x, 2x) (5x+2, x+2, 2x) (5x+2, 2x, x+2)}

= (5x+2) {(1, 2x, 2x) (1, x+2, 2x) (1, 2x, x+2)}

= (5x+2) [(1(x+2)^2 - 4x^2) - 2x(x+2 - 2x) + 2x(2x - x - 2)]

= (5x+2) [(x+2 - 2x)(x+2+2x)-2x(2 - x) + 2x(x-2)]

= (5x+2) [(2-x)(3x+2) -2x(2-x) -2x(2-x)]

= (5x+2) (2-x)[3x+2-2x-2x]

= (5x+2) (2-x)^{2}

QUESTION: 9

Given

Solution:

QUESTION: 10

+ Δ. then Δ is

Solution:

### Determinants Test

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### Determinants Test- 4

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### Determinants Test - 8

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