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Construct a $3 \times 3$ matrix, not in echelon form, whose columns do not span $\mathbb{R}^{3}$ . Show that the matrix you construct has the desired property.

$\left[\begin{array}{lll}{1} & {1} & {1} \\ {0} & {0} & {0} \\ {0} & {1} & {0}\end{array}\right]$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 4

The Matrix Equation Ax D b

Introduction to Matrices

Campbell University

Oregon State University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

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Construct a $3 \times 3$ m…

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If $A$ is an arbitrary $3 …

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All right. So your problem 30. We need to construct a three by three matrix, not in addition form, but whose columns do not spend our three. So that is actually a beauty, eh? Um, a matrix. That column vector. They're the column vectors are they know any dependent? So, too there are many off them, so I'll just try. I just try one. Say I have the column, vector y 12 connective one. And we, let's say, uh, the second column out due to four and negative, too. And Third column. I'll do 36 and negative three. So you can say you can see from from this Matrix, that of the second column is twice off the first column, Third column, third, the third column. He said, um, three times on the first call. So face, make sure excuses three by three matrix, which is, um, clear here. And it is not in the issue of warm, because I have not reduced it yet. And this but this mission is definitely the column. Vectors of columns definitely do not spend our three because we actually we only have one. We only have one vector, and we only have one. Meanwhile, we don't have one people position or people call him So So this this column actors doesn't spend our three at all.

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