Question

find an explicit description of nul a by listing vectors that span the null space. a question content area bottom part 1 a spanning set for nul a is

Answer 1

By using the concept of null space of a matrix, it can be calculated that

Nullspace of A = $\{ \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} , \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}\}$

What is Nullspace of a matrix?

Nullspace of a matrix A is the solution of the equation AX= 0 where 0 is the zero matrix

$\begin{bmatrix} 1 & -3 & 0 & -3 & 0 \\ 0 & 0 & 1 & 4 & 0 \\0 & 0 & 0 & 0 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix}$

We need to find Ax = 0

$\begin{bmatrix} 1 & -3 & 0 & -3 & 0 \\ 0 & 0 & 1 & 4 & 0 \\0 & 0 & 0 & 0 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\0 \end{bmatrix}$

x - 3y - 3w = 0

x = 3y + 3w

z + 4w = 0

z = -4w

-t =  0

t = 0

$\begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix} = \begin{bmatrix} 3y + 3w\\ y \\-4w \\ w\\0 \end{bmatrix}\\\\y \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} + w \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}$

Nullspace of A = $\{ \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} , \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}\}$

To learn more about nullspace of a matrix, refer to the link-

https://brainly.com/question/17484555

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