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Construct a $3 \times 3$ matrix $A,$ with nonzero entries, and a vector $\mathbf{b}$ in $\mathbb{R}^{3}$ such that $\mathbf{b}$ is not in the set spanned by the columnsof $A .$

$A = \left[ \begin{array} { l l l } { 1 } & { 1 } & { 1 } \\ { 1 } & { 1 } & { 1 } \\ { 1 } & { 1 } & { 1 } \end{array} \right]$ and $b = \left[ \begin{array} { l } { 1 } \\ { 2 } \\ { 3 } \end{array} \right]$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

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01:32

In mathematics, the absolu…

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Construct a $3 \times 3$ n…

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Let $S$ be the subspace of…

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Let $A=\left[\begin{array}…

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Prove each of the followin…

Okay, so for problem, tell me too, when you to construct three by three matrix A with none. Zero entries and a veteran be in our three, such that he's not set Spend by columns of a So he's sexually just to construct a matrix A and Victor bees such that the system is inconsistent. So there are a lot of matrices and vectors like this. I'll just give give my own matrix and you can try your own parcel So many trees high gave it so that will be one neck of three and two and or one fight and 271 And the vector B, I consider is next. If I 11 elective seven Okay, just to just to show why this, uh, why's this system is inconsistent is you just need to consider the argumentative Matrix. So his case, it will be one left of three and two and five. Sorry, negative. Five and four or one high. And 11 271 active seven. So if we if you do the you do the couching elimination and to find out a Rory to station form, then I'll just write it down here. So the real redo station form will be 10 17 3rd and zero second. Rory is 01 like 23 13 and zero. So that's rule 000 And the one so clearly this term on the third row should not be one. Because we have all zero back already. There is on the left inside. And if we are given any vector, the nef s I will always be zero. But the right hand side is accounts in one, so the system is not consistent in this case.

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