Important Questions with Class 12 Maths Chapter 3 – Matrices Solutions

1) Calculate the value of x – y, if

Ans – Given that,

Both matrices are equivalent here, hence we equate the corresponding elements,
2 + y = 5
2x + 2 = 8
⇒ y = 3
⇒ 2x = 6 ⇒ x = 6/2 = 3
∴ x – y = 3 – 3 = 0

then write the order of matrix A.

Ans –

= [- 3 – I]
= [- 4]1 × 1
∴ matrix A will be of order 1 × 1.

By equating the appropriate elements, we obtain
8 + y = 0
2x + 1 = 5
⇒ y = – 8
⇒ x = (5−1)/2 = 2
∴ x – y = 2 – (-8) = 10

Ans – At first, multiply each member of the first matrix by cos θ and each element of the second matrix by sin θ, followed by performing matrix addition.

5) Determine a matrix A such that 2A – 3B + 5C = 0, where

Ans – It is given that 2A – 3B + 5C = 0
⇒ 2A = 3B – 5C

6) Calculate A² – 5A + 4I and thereafter determine a matrix X such that A² – 5A + 4I + X = 0, where

Ans – Given matrix A.

7) Find the value of k if A³ – 6A² + 7A + kI₃ = 0, where

Ans – Given matrix A.

NCERT Matrices Chapter 3 – Class 12 Maths

In mathematics, particularly in class 12, matrices are quite important in many different uses. A basic subject with practical uses in domains including computer science, economics, and engineering as well as forming the foundation of many mathematical ideas is matrix theory. Students must have a firm grasp of matrices if they want to succeed in their studies as they work through their class 12 course.

Matrices’ value in Class 12

In class 12 mathematics, matrices are used for data in an organised form, transformations, and system of equation solving. Students who want to grasp subjects such determinants, inverse matrices, and matrix multiplication must first understand matrices. Furthermore, matrices are a useful tool for students to master since they help them to address practical issues.

Why Important Questions Matter?

Practicing key questions on matrices can help students increase their problem-solving abilities and confidence in the topic as they get ready for their class 12 exams. Important questions are especially chosen to address the main ideas and subjects that will probably come up on tests. Through regular practice of these questions, students can become familiar with the test structure, strengthen their matrix knowledge, and raise their general performance.