If A = [[1, 3], [3, 4]] and B = [[-2, 1], [-3, 2]] and A² - 5B² = 5C. Find matrix C, where C is a 2 by 2 matrix.

Topic: Matrices

Previous-year question practice database

Answer

Exam answer

A = [[1,3],[3,4]] B = [[−2,1],[−3,2]].

A² = [[10,15],[15,25]].

B² = [[1,0],[0,1]].

Given:

A² − 5B² = 5C.

5C = [[10,15],[15,25]] − [[5,0],[0,5]] = [[5,15],[15,20]].

C = [[1,3],[3,4]].

Answer: C = [[1,3],[3,4]].

Explanation

Calculate A² and B² by row-by-column multiplication, subtract 5B², then divide each entry by 5.