Given matrix B = [[1, 1], [8, 3]], find the matrix X if X = B² - 4B. Hence solve for a and b given X * [[a], [b]] = [[5], [50]].

Topic: Matrices

Previous-year question practice database

Answer

Exam answer

B = [[1,1],[8,3]].

B² = [[9,4],[32,17]].

4B = [[4,4],[32,12]].

X = B² − 4B = [[5,0],[0,5]].

Given:

X[[a],[b]] = [[5],[50]].

[[5a],[5b]] = [[5],[50]].

a = 1, b = 10.

Answer: X = [[5,0],[0,5]], a = 1, b = 10.

Explanation

Calculate B², subtract 4B, then multiply X by the column vector and equate corresponding entries.