Class XII Physics: Matrix Operations

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Questions and Answers

What is the inverse of matrix A?

A⁻¹

What is the inverse of AB?

(AB)⁻¹

If matrix m is equal to n, what is the value of A?

If matrix A = [3 6] and matrix B = [7 8], what is the value of 2A + 3B?

[31 42] Signup and view all the answers

If matrix A = [9 10 11] and matrix B = [8 10 9], what is the value of A + B?

[17 20 20] Signup and view all the answers

If the determinant of a 2x2 matrix is 11, what is the determinant of the inverse of that matrix?

1/11 Signup and view all the answers

If A = [aᵢⱼ] and matrix A is a square matrix of m rows, what is the determinant of A?

det(A) Signup and view all the answers

If A = [0 0] and matrix A is a square matrix of n rows, what is the value of A² + 3A + 2I?

2I Signup and view all the answers

If [2x - y 5] = [6 5] , what is the value of x?

x = 3 Signup and view all the answers

If 3x + y = [7 0] and x - y = [3 3], what is the value of x?

x = 2.5 Signup and view all the answers

If A = [5 1] and B = [6 7], what is the value of A - B?

[-1 -6] Signup and view all the answers

If A = [3 5] and I = [1 0], what is the value of 7I?

[7 0] Signup and view all the answers

If A = [a b] and A is an empty matrix, what is the value of A?

A is an empty matrix Signup and view all the answers

If A = [1 1 1] , what is the value of Aᵀ?

Aᵀ = [1 1 1] Signup and view all the answers

If A = [9 0] and B = [1 5], what is the value of A² - B ?

[81 -25] Signup and view all the answers

What is the coefficient matrix of the following system of equations: 2x + 0y - 1z = 2, 5x + 1y + 0z = 4,0x + 0y + 3z = 2?

[2 0 -1],[5 1 0],[0 0 3] Signup and view all the answers

What is the value of x,y,z that satisfy the system of equations: x + y + 2z = 9, x + 2z = 5, y + 2z = 7?

x = 1, y = 3, z = 2 Signup and view all the answers

What is the value of the determinant of [2 3 4]

1 Signup and view all the answers

What are the values of the determinant of matrix [2 3] and [2 3 1]

The determinant of [2 3] is 1, and the determinant of [2 3 1] is -1 Signup and view all the answers

What is the value of |cosθ sinθ| + |sinθ cosθ|

1 Signup and view all the answers

If A= [5/2], what is the value of A'?

A' = [5/2] Signup and view all the answers

Given matrix A, what is the value of |A|?

|A| Signup and view all the answers

Study Notes

Class XII Physics Notes

Problem Solving: All problems are mandatory

Matrix Operations

Definition of Transpose: A' is the transpose of matrix A
Definition of Inverse: (AB)' = B'A'
Definition of Matrix Addition: (A+B)' = A' + B'
Definition of Matrix Multiplication: (A')' = A
Matrix Example: A = [3 6] B=[8]
Matrix Example: If m=n then A is a square matrix

Matrix Problem Solving

Problem 1: Find the value of 'A'
Problem 2: Given Matrix A = [2/3 4], find A²
Problem 3: Solve the simultaneous equation 2x-y = 3 and x+y = 2
Problem 4 Find the value of x and y
Problem 5: Find the value of x
Problem 6: A = [ 5 7 ], B = [], find AB
Problem 7: Determine if Matrix A = [ 3 5] is a symmetric or skew-symmetric matrix
Problem 8: A = [ ... ] find A²
Problem 9: Given A = [ 9 0 ] , B = [ 0 5 ] , find A² – B²
Problem 10: Solve [ 2 0 -1] and [ 5/3 1 0]
Problem 11: Find the values of x and y ,given √[(x+y+2)/(x+2)] = √[(3/5)] and√[(y+2)/(y+2)]=√[(7/5)]
Problem 12: Solve √[2/3] [2 3 4 ]
Problem 13: Simplify – cosθ sinθ + sinθ cosθ
Problem 14: (i) Find the value of A' and (ii) solve for [2/3] [2/3 3/4] for a matrix with 24 elements

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Description

Test your understanding of matrix operations covered in Class XII Physics. This quiz offers problems that will challenge your skills in matrix addition, multiplication, and finding inverses. Solve various problems to master the concepts and applications of matrix theory.