Test: Minors And Cofactors - JEE MCQ

# Test: Minors And Cofactors - JEE MCQ

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## 10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Minors And Cofactors

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Test: Minors And Cofactors - Question 1

### Inverse of a matrix A exists, if​

Detailed Solution for Test: Minors And Cofactors - Question 1

Only non-singular matrices have inverses.
Suppose that A is invertible. This means that we have the inverse matrix A−1 of A.
Consider the equation Ax=0. We show that this equation has only zero solution.
Multiplying it by　A−1 on the left, we obtain
A−1 Ax = A-1
⇒ x = 0

Test: Minors And Cofactors - Question 2

### If A =  , and |3A| = k|A|, then the value of k is

Detailed Solution for Test: Minors And Cofactors - Question 2

|kA| = kn|A|
|3A| = (3)n |A|
= 27|A| = k|A|
k = 27

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Test: Minors And Cofactors - Question 3

### Find the value of

Detailed Solution for Test: Minors And Cofactors - Question 3

Correct Answer :- d

Explanation:- 3(6-6) -2(6-9) +3(4-6)

= 3(0) + 6 - 6

= 0

Test: Minors And Cofactors - Question 4

If A =, then adj A is:

Test: Minors And Cofactors - Question 5

The cofactor of an element 9 of the determinant   is :

Detailed Solution for Test: Minors And Cofactors - Question 5

Co factor of element 9 will be {(6 * 8) -(-5 * 0)}
= 48

Test: Minors And Cofactors - Question 6

The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the​

Detailed Solution for Test: Minors And Cofactors - Question 6

A minor, Mij, of the element aij is the determinant of the matrix obtained by deleting the ith row and jth column.

Test: Minors And Cofactors - Question 7

The cofactor of 5 in

Detailed Solution for Test: Minors And Cofactors - Question 7

A21 = {(0, -1) (3,4)}
⇒ (0 - (-3)) = 3
A21 = (-1)(2+1) (3)
= -3

Test: Minors And Cofactors - Question 8

If , then the relation between x and y is

Detailed Solution for Test: Minors And Cofactors - Question 8

½{(0,0,1) (1,3,1) (x,y,1)} = 0
{(0,0,1) (1,3,1) (x,y,1)} = 0/(½)
{(0,0,1) (1,3,1) (x,y,1)} = 0
0(3-y) -0(1-x) +1(y-3x) = 0
=> y - 3x = 0
=> y = 3x

Test: Minors And Cofactors - Question 9

If matrix A =   and A2 + aA + b = O, then the values of a and b are:

Test: Minors And Cofactors - Question 10

If   and Aij are cofactors of aij, then

Detailed Solution for Test: Minors And Cofactors - Question 10

Δ = Sum of products of element of row(or column)  with their corresponding co-factors.
Δ = a11 A11 + a21 A21 + a31 A31

## Mathematics (Maths) for JEE Main & Advanced

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests