If A = [[2, 1], [0, 3]], B = [[0, 1], [-1, 2]] and C = [[1, -1], [2, 0]], find AC + B² - 10C.

Topic: Matrices

Previous-year question practice database

Answer

Exam answer

A = [[2,1],[0,3]] B = [[0,1],[−1,2]] C = [[1,−1],[2,0]].

AC = [[4,−2],[6,0]]. B² = [[−1,2],[−2,3]]. 10C = [[10,−10],[20,0]].

AC + B² − 10C = [[−7,10],[−16,3]].

Answer: [[−7,10],[−16,3]].

Explanation

Compute AC and B² by row-column multiplication, then subtract 10C entrywise.