12th Maths Guide Solution Chapter 1 Application Of Matrices and Determinants Exercise 1.1

Here are the Class 12th maths guide solutions of Chapter 1 Application of Matrices and Determinants Exercise 1.1, according to the Samacheer Kalvi syllabus for Tamil Nadu state board students.

Maths Questions and Answer Solution in PDF for 12th class Tamil Nadu state board students, Samacheer Kalvi Syllabus

Below are the questions and answer notes in PDF for the Tamil Nadu State Board 12th class students according to the Samacheer Kalvi syllabus.

Question No. 1: Find the adjoint of the following.

Solution:-

Question No 2: Find the inverse (if it exists) of the following.

Solution:

|A| = 2 (8-7) -3 (6-3)+1 (21-12)
= 2 – 9 + 9 = 2 ≠ 0. A^-1  exists.

Question No 3:

Solution:-

|F(α)| = cos α(cos α – 0) – 0 + sin α(0 + sin α)
= cos²α + sin²α = 1
|f(α)| = 1 ≠ 0. [F(α)]^-1 exists.

[cos (-θ) = cos θ ; sin(-θ) = -sin θ]
from (1) and (2) we have
[F(α)]^-1 = F(-α)

Question No 4:

Solution:-

A² – 3A – 7I₂  = O₂
Post multiply this equation by A^-1
A² A^-1 – 3A A^-1 – 7I₂ A^-1 = 0
A – 3I – 7A^-1 = 0
A – 3I = 7 A^-1
A^-1 = 17 (A – 3I)

Question No 5:

Solution:

Question No 6:

Solution:-

(1) (2) and (3) ⇒ A (adj A) = (adj A)A = |A| I₂.

Question No 7:

Solution:

Question No 8:

Solution:

|adj (A)| = 2 (24 – 0) + 4 (- 6 – 14) + 2(0 + 24)
= 48 – 80 + 48 = 16

Question No 9:

Solution:-

Question No 10:

Question No 11:

Hence Proved.

Question No 12:

Solution:-

Question No 13:

Solution:-

Given A × B × C
⇒ A^-1 A × B B^-1 = A^-1 C B^-1
I × I = A^-1 C B^-1
⇒ X = A^-1 CB^-1
let us find A^-1 and B^-1

Question No 14:

Solution:-

Hence Proved.

Question No 15:

Solution:-

So the sequence of decoded row matrics is [8 5] [12 16]
The receiver reads the message as “HELP”.