Advertisements
Advertisements
Question
If A = `[(1, 0),(2, 1)], B = [(2, 3),(-1, 0)]`, find A2 + B2 + AB.
Sum
Advertisements
Solution
A = `[(1, 0),(2, 1)], B = [(2, 3),(-1, 0)]`
A2 = `[(1, 0),(2, 1)] [(1, 0),(2, 1)]`
= `[(1 xx 1 + 0 xx 2, 1 xx 0 + 0 xx 1),(2 xx 1 + 1 xx 2, 2 xx 0 + 1 xx 1)]`
= `[(1, 0),(4, 1)]`
B2 = `[(2, 3),(-1, 0)] [(2, 3),(-1, 0)]`
= `[(2 xx 2 + 3 xx (-1), 2 xx 3 + 3 xx 0),(-1 xx 2 + 0 xx (-1), (-1) xx 3 + 0 xx 0)]`
= `[(1, 6),(-2, -3)]`
AB = `[(1, 0),(2, 1)] [(2, 3),(-1, 0)]`
= `[(1 xx 2 + 0 xx (-1), 1 xx 3 + 0 xx 0),(2 xx 2 + 1 xx (-1), 2 xx 3 + 1 xx 0)]`
= `[(2, 3),(3, 6)]`
A2 + B2 + AB = `[(1, 0),(4, 1)] + [(1, 6),(-2, -3)] + [(2, 3),(3, 6)]`
= `[(1 + 1 + 2, 0 + 6 + 3),(4 - 2 + 3, 1 - 3 + 6)]`
= `[(4, 9),(5, 4)]`
shaalaa.com
Is there an error in this question or solution?
Chapter 8: Matrices - Exercise 8C [Page 164]
