AI Tutor
Back to Matrix Multiplication

Exercise 24

Avg difficulty 3.0

Recall the notation for the sum of the sequence of numbers a1,a2,…,ana_{1},a_{2},\dots,a_{n}.

∑i=1nai=a1+a2+⋯+an\sum_{i=1}^{n}a_{i}=a_{1}+a_{2}+\dots+a_{n}

In this notation, the i,ji,j entry of the product of GG and HH is this.

pi,j=∑k=1rgi,khk,jp_{i,j}=\sum_{k=1}^{r}g_{i,k}h_{k,j}

Using this notation,

  • reprove that matrix multiplication is associative;

  • reprove Theorem 2.7.

Hefferon, Linear Algebra, Maps Between Spaces, Matrix Multiplication, Exercise 24

AI Tutor

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