Find a Basis for the Null Space of the Matrix $$A = \left[ \begin{array} { r r r r } 1 & 0 & - 7 & - 4 \\0 & 1 & 5 & - 2 \\0 & 0 & 0 & 0\end{array} \right]$$

question 70

Multiple Choice

Find a basis for the null space of the matrix.
- $$A = \left[ \begin{array} { r r r r } 1 & 0 & - 7 & - 4 \\0 & 1 & 5 & - 2 \\0 & 0 & 0 & 0\end{array} \right]$$

• A)\[\left\{ \left[ \begin{array} { l }
• 1 \\
• 0 \\
• 0
• \end{array} \right] , \left[ \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right] \right\}\]
• B)
• \[\left\{ \left[ \begin{array} { r }
• - 7 \\
• 5 \\
• 1 \\
• 0
• \end{array} \right] , \left[ \begin{array} { r }
• - 4 \\
• - 2 \\
• 0 \\
• 1
• \end{array} \right] \right\}\]
• C)
• \(\left\{\left[\begin{array}{r}
• 7 \\
• -5 \\
• 1 \\
• 0
• \end{array}\right],\left[\begin{array}{l}
• 4 \\
• 2 \\
• 0 \\
• 1
• \end{array}\right]\right\}\)
• D)
• \(\left\{\left[\begin{array}{r}
• 1 \\
• 0 \\
• -7 \\
• -4
• \end{array}\right],\left[\begin{array}{r}
• 0 \\
• 1 \\
• 5 \\
• -2
• \end{array}\right]\right\}\)

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Definitions:

Switch Statement

A control statement that allows a variable to be tested for equality against a list of values, each with its own case block of code.

Repetition Statement

A programming construct that allows for the repeated execution of a block of code for a specified number of times or while a condition is true.

While Statement

A control flow statement that allows code to be executed repeatedly based on a given Boolean condition.

Expression

A combination of variables, operations, and values that produces another value.