Question

which of these matrices are zero matrices? select all that apply.
\\(\

$$\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}$$

\\) \\(\

$$\begin{bmatrix}0&0\\end{bmatrix}$$

\\) \\(\

$$\begin{bmatrix}1&0&0\\\\0&1&0\\\\0&0&1\\end{bmatrix}$$

\\)
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Explanation:

Step1: Recall zero matrix definition

A zero matrix has all entries as \(0\).

Step2: Analyze first matrix

\(

$$\begin{bmatrix}0&0\\0&0\end{bmatrix}$$

\): All entries are \(0\), so it is a zero matrix.

Step3: Analyze second matrix

\(

$$\begin{bmatrix}0&0\end{bmatrix}$$

\): All entries are \(0\), so it is a zero matrix.

Step4: Analyze third matrix

\(

$$\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$$

\): Entries are \(1\) (diagonal) and \(0\) (non - diagonal), not all \(0\), so not a zero matrix.

Answer:

The correct zero matrices are the first matrix \(\boldsymbol{

$$\begin{bmatrix}0&0\\0&0\end{bmatrix}$$

}\) and the second matrix \(\boldsymbol{

$$\begin{bmatrix}0&0\end{bmatrix}$$

}\) (the third matrix is the identity matrix, not a zero matrix). So the correct selections should be the first two matrices (the \(2\times2\) zero matrix and the \(1\times2\) zero matrix), and the third matrix should not be selected.