How do you simplify #3[(2,7),(-3,6)]+5[(-6,-4),(3,0)]#?

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Answer 1 · 2017-05-26T14:55:21

#[(-24, 1), (6, 18)]#

Use this matrix concept: #k [(a, b), (c, d)] = [(ka, kb), (kc, kd)]#

Matrices of the same size/dimension can be added:

#[(a, b), (c, d)] + [(e, f), (g, h)] = [(a+e, b+f), (c+g, d+h)]#

Given: #3 [(2, 7), (-3, 6)] + 5[(-6, -4), (3, 0)]#

Multiple by the constants:

#3 [(2, 7), (-3, 6)] = [(6, 21), (-9, 18)]#

#5[(-6, -4), (3, 0)] = [(-30, -20), (15, 0)]#

Add the two new matrices:

#[(6, 21), (-9, 18)] + [(-30, -20), (15, 0)] = [(-24, 1), (6, 18)]#