Question

Properties of matrices RA^(5) If F=[[2],[-2],[-5]],G=[[6],[-4],[2]], and H=[[7,6,-5]], is the following statement true or false? (F+G)H=FH+GH

Answer 1

The statement (F+G)H=FH+GH is false.

Step-by-step explanation:

To determine if the statement (F+G)H=FH+GH is true or false, we need to perform the matrix operations on the given matrices. Firstly, we can find (F+G) by adding F and G element-wise. (F+G) = [[2+6],[-2+(-4)],[-5+2]] = [[8],[-6],[-3]]. Next, we can compute FH and GH by multiplying F and H, and G and H, respectively. FH = [[2, -2, -5]] * [[7],[6],[-5]] = [[14+(-12)+25]] = [[27]]. GH = [[6, -4, 2]] * [[7],[6],[-5]] = [[42+(-24)+(-10)]] = [[8]]. Therefore, we have (F+G)H = [[8],[-6],[-3]] * [[7],[6],[-5]] = [[27+(-18)+15],[-42+36-30],[21+(-18)+15]] = [[24],[-36],[18]]. Moreover, we have FH+GH = [[27]]+[[8]] = [[27+8]] = [[35]]. Since (F+G)H is not equal to FH+GH, the statement (F+G)H=FH+GH is false.