NumericalHard3 marks
7(c)
Given [[4, 2], [-1, 1]] M = 6I, where M is a matrix and I is unit matrix of order 2×2.
Find the matrix M.
Topic: Matrices
Previous-year question practice database
Answer
Exam answer
Let M = [[a,b],[c,d]].
[[4,2],[−1,1]][[a,b],[c,d]] = [[6,0],[0,6]].
Thus: 4a+2c=6 −a+c=0 ⇒ a=1, c=1.
4b+2d=0 −b+d=6 ⇒ b=−2, d=4.
Answer:
M = [[1,−2],[1,4]].
Explanation
Multiply row by column and equate corresponding entries with 6I.