12th mex1

 

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.1

12th Maths Exercise 1.1 Answers Question 1.
Find the adjoint of the following:

Solution:

Exercise 1.1 Class 12 Maths State Board Question 2.
Find the inverse (if it exists) of the following:

Solution:
For a matrix A, A−1=1|A|(adjA). Where |A| ≠ 0. If |A| = 0 then A is called a singular matrix and so A−1 does not exist.

12th Maths Exercise 1.1 Question 3.
If F(α) = ⎡⎣⎢cosα0−sinα010sinα0cosα⎤⎦⎥ show that [F(α)]−1=F(−α)
Solution:
Let A = F (α)
So [F(α)]−1=A−1
Now

12th Maths Chapter 1 Exercise 1.1 Question 4.
If A = [5−13−2] show that A2 – 3A – 7I2 = O2. Hence find A-1.
Solution:
A = [5−13−2]

To Find A-1
Now we have proved that A2 – 3A – 7I2 = O2
Post multiply by A-1 we get
A – 3I – 7A-1 = O2

12th Maths 1.1 Exercise Question 5.
If A=19⎡⎣⎢−84114−8474⎤⎦⎥ prove that A-1 = AT
Solution:

12 Maths Exercise 1.1 Question 6.
If A=[8−5−43], verify that A(adj A) = (adj A)A = |A| I2
Solution:

12th Maths 1st Chapter Exercise 1.1 Question 7.
If A=[3725], and B=[−15−32] verify that (AB)-1 = B-1 A-1.
Solution:

12th Maths Application Of Matrices And Determinants Question 8.
If adj (A) = ⎡⎣⎢2−3−2−41202−72⎤⎦⎥ find A
Solution:

12th Maths Ex 1.1 Question 9.
If adj(A) = ⎡⎣⎢06−3−2200−66⎤⎦⎥ find A-1
Solution:

12th Exercise 1.1 Question 10.
Find adj(adj(A)) if adj A = ⎡⎣⎢10−1020101⎤⎦⎥
Solution:

12th Maths Exercise 1.1 Answers In Tamil Medium Question 11.

Solution:

12th Maths 1st Chapter Question 12.
Find the matrix A for which A [5−13−2]=[14777]
Solution:
Given A [5−13−2]=[14777]
Let B=(5−13−2) and C=(14777)
Given AB = C, To find A
Now AB = C
Post multiply by B-1 on both sides
ABB-1 = CB-1 (i.e) A (BB-1) = CB-1
⇒ A(I) = CB-1 (i.e) A = CB-1
To find B-1:

12th Maths 1.1 Question 13.
Given A=[12−10],B=[31−21] and C[1212], find a matrix X such that AXB = C.
Solution:
A × B = C
Pre multiply by A-1 and post multiply by B-1 we get
A-1 A × BB-1 = A-1CB-1 (i.e) X = A-1CB-1

12 Maths Samacheer Kalvi Solutions Question 14.

Solution:

12th Maths Exercise 1.1 5th Sum Question 15.
Decrypt the received encoded message [2−3][204] with the encryption matrix [−12−11] and the decryption matrix as its inverse, where the system of codes are described by the numbers 1-26 to the letters A- Z respectively, and the number 0 to a blank space.
Solution:
Let the encoding matrix be [−12−11]


So the sequence of decoded matrices is [8 5], [12 16].
Thus the receivers read this message as HELP.

Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.1 Additional Problems

12th Maths Chapter 1 Question 1.
Using elementary transformations find the inverse of the following matrix 
Solution:

12th Maths Guide Question 2.
Using elementary transformations find the inverse of the matrix 
Solution:

12th Maths Solutions Samacheer Kalvi Question 3.
Using elementary transformation find the inverse of the matrix 
Solution:

12 Maths Chapter 1 Exercise 1.1 Question 4.
Using elementary transformations find the inverse of the matrix 
Solution:

12th Maths Exercise 1.1 Solutions Question 5.
Using elementary transformation, find the inverse of the following matrix 
Solution:

Samacheer Kalvi 12th Maths Guide Question 6.

Solution:

Samacheer Kalvi 12 Maths Solutions Question 7.

Solution:

12 Maths Solutions Samacheer Kalvi Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution: