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Mathematics MCQ - Vectors and Matrices

61 Inverse of the matrix

Inverse of the matrix

A
B
C
D

For the matrix

Linear Algebra

cofactors are

a₁₁= 1, a₂₁ = -5, a₁₂= -2, a₂₂= -3

Therefore matrix by cofactors

Linear Algebra

Adjoint A

Linear Algebra

I A I = -3(1) - 5(2)

= -3 - 10

= -13

Linear Algebra

62 If A and B are square matrices of size n × n ,

then which of the following statement is not true?

63 If A be an invertible matrix and inverse of 7A is

If A be an invertible matrix and inverse of 7A is

then matrix A is

A
B
C
D

Inverse of 7A=

Linear Algebra

Linear Algebra

= 7 - 8 = -1

Therefore matrices of co factor

Linear Algebra

and its transpose,

Linear Algebra

64 If A =

then state transition matrix eAt is

then state transition matrix eA^t is

A
B
C
D

Here,

Linear Algebra

65 For the matrix

one of the eigen values is equal to -2 which of the following is an eigen vector

one of the eigen values is equal to -2.

which of the following is an eigen vector?

A
B
C
D

Linear Algebra

Putting λ= -2, we get 5x--2y+2z = 0

Putting z = 0, we get 5x = 2y

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Day 3 / 10

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Question:

Rank of the matrix A = 0 0 0 0 4 2 3 0 1 0 0 0 4 0 3 0

Answer:

Determinant A = 0 ⇒ 4 2 3 1 0 0 4 0 3 Hence rank of A=3

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