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Exercise 13

Avg difficulty 3.0

  • How does matrix multiplication interact with scalar multiplication: is r(GH)=(rG)Hr(GH)=(rG)H? Is G(rH)=r(GH)G(rH)=r(GH)?

  • How does matrix multiplication interact with linear combinations: is F(rG+sH)=r(FG)+s(FH)F(rG+sH)=r(FG)+s(FH)? Is (rF+sG)H=rFH+sGH(rF+sG)H=rFH+sGH?

Hefferon, Linear Algebra, Maps Between Spaces, Matrix Multiplication, Exercise 13

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.