If adj(A) = [2-42-312-7-202], find A - Mathematics

Question

If adj(A) = `[(2, -4, 2),(-3, 12, -7),(-2, 0, 2)]`, find A

Sum

Solution

adj(A) = `[(2, -4, 2),(-3, 12, -7),(-2, 0, 2)]`

A = `+- 1/sqrt(+"adj A"|)` adj (adj A)

|adj (A)| = 2(24 – 0) + 4(– 6 – 14) + 2(0 + 24)

= 48 – 80 + 48

= 16

adj (adj A) = `[(+|(12, - 7),(0, 2)|, -|(-3, - 7),(-2, 2)|, +|(-3, 12),(-2, 0)|),(-|(-4, 2),(0, 2)|, +|(2, 2),(-2, 2)|, -|(2, -4),(-2, 0)|),(+|(-4, 2),(12, -7)|, -|(2, 2),(-3, -7)|, +|(2, -4),(-3, 12)|)]^"T"`

= `[(+(24 - 0), -(-6 - 14), +(0 + 24)), (-(- 8 - 0), +(4 + 4), -(0 - 8)),(+(28 - 24), -(- 14 + 6), +(24 - 12))]^"T"`

= `[(24, 20, 24),(8, 8, 8),(4, 8, 12)]^"T"`

adj (adj A) = `[(24, 8, 4),(20, 8, 8),(4, 8, 12)]`

= `4[(6, 2, 1),(5, 2, 2),(6, 2, 3)]`

`sqrt(|"adj A"|) = sqrt(16)` = 4

A = `+- (1/4) 4[(6, 2, 1),(5, 2, 2),(6, 2, 3)]`

= `+- [(6, 2, 1),(5, 2, 2),(6, 2, 3)]`

shaalaa.com

Inverse of a Non-singular Square Matrix

Is there an error in this question or solution?

Q 8 Q 7 Q 9

Chapter 1: Applications of Matrices and Determinants - Exercise 1.1 [Page 16]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board

Chapter 1 Applications of Matrices and Determinants
Exercise 1.1 | Q 8 | Page 16

RELATED QUESTIONS

Find the adjoint of the following:

`[(-3, 4),(6,2)]`

Find the adjoint of the following:

`[(2, 3, 1),(3, 4, 1),(3, 7, 2)]`

Find the adjoint of the following:`1/3[(2, 2, 1),(-2, 1, 2),(1, -2, 2)]`

Find the inverse (if it exists) of the following:

`[(2, 3, 1),(3, 4, 1),(3, 7, 2)]`

If A = `[(5, 3),(-1, -2)]`, show that A² – 3A – 7I₂ = O₂. Hence find A^–1

If A = `[(8, -4),(-5, 3)]`, verify that A(adj A) = (adj A)A = |A|I₂

Find adj(adj(A)) if adj A = `[(1, 0, 1),(0, 2, 0),(-1, 0, 1)]`

A = `[(1, tanx),(-tanx, 1)]`, show that A^T A^–1 = `[(cos 2x, - sin 2x),(sin 2x, cos 2x)]`

Given A = `[(1, -1),(2, 0)]`, B = `[(3, -2),(1, 1)]` and C = `[(1, 1),(2, 2)]`, find a martix X such that AXB = C

If A = `[(0, 1, 1),(1, 0, 1),(1, 1, 0)]`, show that `"A"^-1 = 1/2("A"^2 - 3"I")`