Determinants Test

Result

Determinants Test - 3

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Question 1
1 / -0.25

Let a = , then Det. A is

A
0

B
ab +bc+ca

C
1+ab+bc+ca

D
none of these

Solution

Apply C₂ →C₂ + C_3,
Question 2
1 / -0.25

A
x = 2 or 6

B
x = 4 or 3

C
x = 2

D
none of these

Solution

because , the value of the determinant is zero only when , the two of its rows are identical., Which is possible only when Either x = 3 or x = 4 .
Question 3
1 / -0.25

A
−2(a+b+c )³

B
2(a+b+c)²

C
4(a+b+c)³

D
none of these

Solution

Apply , R₁ →R₁ +R₂ +R₃ ,

Apply , C₃ →C₃ - C₁ , C₂^→ C₂ - C₁ ,
=(a+b+c)³
Question 4
1 / -0.25

If A and B matrices are of same order and A + B = B + A, this law is known as

A
distributive law

B
commutative law

C
associative law

D
cramer 's law

Solution

Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba
Question 5
1 / -0.25

If A ’is the transpose of a square matrix A , then

A
|A| ≠|A ′|

B
|A|+|A ′| = 0

C
|A| = |A ′|

D
none of these

Solution

The determinant of a matrix A and its transpose always same.
Question 6
1 / -0.25

The value of the determinant is

A
1+a+b+c

B
a+b+c

C
0

D
none of these

Solution

, Apply , C₂ →C₂ + C₃

= 0, (∵C₁ = C₂ )
Question 7
1 / -0.25

The roots of the equation det. are

A
1 , 2, and 3

B
1 and 3

C
2, and 3

D
none of these.

Solution

⇒(1-x)(2-x)(3-x) = 0 ⇒x = 1,2,3
Question 8
1 / -0.25

If A is a square matrix of order 2 , then det (adj A) = x

A
|A|.

B
I

C
A² = O

D
2A²

Solution

Let A be a square matrix of order 2 . then ,|adj.A| = |A|
Question 9
1 / -0.25

If A is a symmetric matrix, then A^t =

A
A

B
|A|

C
0

D
diagonal matrix

Solution

If A is a symmetric matrix then by definition AT=A
Option A is correct.
Question 10
1 / -0.25

A
0

B
3e

C
2

D
none of these

Solution

, because , row 1 and row 3 are identical.