Previous-year question practice database
Answer
Exam answer
Given:
A = [[3,1],[5,3]] B = [[−1,a],[3,−5]] AB = [[b,7],[4,5]]
AB = [[3(−1)+1(3), 3a−5], [5(−1)+3(3), 5a−15]] = [[0, 3a−5], [4, 5a−15]].
Equating corresponding entries: b = 0 3a−5 = 7 3a = 12 a = 4.
Check: 5(4)−15 = 5.
Answer: a = 4, b = 0.
Explanation
Multiply matrices row by column, then equate corresponding entries with the given product matrix.