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Compute the products in Exercises $1-4$ using $(\mathrm{a})$ the definition, as in Example $1,$ and $(\mathrm{b})$ the row-vector rule for computing $A \mathrm{x}$ . If a product is undefined, explain why.$$\left[\begin{array}{r}{2} \\ {6} \\ {-1}\end{array}\right]\left[\begin{array}{r}{5} \\ {-1}\end{array}\right]$$

product is undefined

00:30

Runpeng L.

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 4

The Matrix Equation Ax D b

Introduction to Matrices

Missouri State University

McMaster University

Harvey Mudd College

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So before we even try to multiply this, you might just try to write down the size of each of these matrices just to see if we can. So the way we right a matrix is it's the number of rows, then the columns. So this first one, so it has three rows that is gonna be a three by one matrix. And then over here, this has two rows. One column. So this is gonna be a two by one matrix. And remember, for us to be able to multiply any matrices or to be defined, these two need to be the same. But in this case, since they're not the same, then we're going to have where this isn't undefined product. Now, the way I normally think about this, I don't really even look at the size. What I do is I go across the first row and then the first column of the second one, and I just see if these air of the same length or not. So over here I have a length one here. I have length to so same thing not equal. So I mean the same ideas. Writing out the whole matrix But we're really only interested in the length of the first row and then the length of the first column like that. Yeah, so if you do either of these ways here, I'd say it's more standard to just write down the size of the matrices and then see if those first two numbers match. And in this case, since they don't match, we have no product.

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