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Suppose the second column of $B$ is all zeros. What can you say about the second column of $A B ?$

If the second column of B is all Zeros, then the second column of AB will also be all Zeros

Algebra

Chapter 2

Matrix Algebra

Section 1

Matrix Operations

Introduction to Matrices

Campbell University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

01:46

Suppose the last column of…

01:17

Suppose the third column o…

03:19

Suppose the first two colu…

02:19

Suppose the matrix represe…

02:33

Suppose $a, b, c,$ and $d$…

02:44

If $\mathbf{A}+\mathbf{B}$…

01:00

If $\mathbf{A}+\mathbf{B}=…

02:03

Can you explain whether a …

02:35

Find $A B$ and $B A$ in ea…

02:17

If $A=\left[\begin{array}{…

Okay, so here were asked to comment on the product. A Times B If the second column of B is entirely zero, and we're gonna use the fact that each column of the product A B is a linear combination of the columns of a using the corresponding column of B as weights. So what that means is, if I write a be sub to here, meaning the second column of the Matrix AIDS has B that's gonna be equal to the first column. Obey. Plus, um, the second column of a plus, the third going away and so on using be, ah, throw one calling, too, and then be to to and be 33 year 232 as weights. So the call in vectors of a here are what we're taking the letter combination or the linear combination of and the elements of the second column of B R. What we use is the weights in that linear combination, and what that means is, if b I, too, is equal to zero for ah, I going from one way to end, then that means that this a B two will also be entirely zero right, because we're multiplying it by zero each time for each. Each column vector then will be multiplied by zero, and we'll get Aaaah this year a vector.

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