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Linear Algebra

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Matrix Combinations

LINALG-TSWEGG

Let:

$$A=\left [\matrix { 2 & -1 & 1\cr 0 & 3 & 1\cr 1 & 2 & 4}\right ]$$

Let:

$$\vec b=\left [\matrix { 1 & 2 & 4}\right ]$$

Determine which of the following statements are TRUE.

Select ALL that apply.

A

$\vec b$ can be written as a linear combination of the columns of $A$.

B

$\vec b$ can be written as a linear combination of the rows of $A$.

C

The first column of the matrix $A$ can be written as a linear combination of the other two columns of $A$.

D

None of the above are true.