which matrix is equal to $\begin{bmatrix}3&2\\-5&9end{bmatrix}$?\n$\begin{bmatrix}3&2&-5&9end{bmatrix}$\n$\be…

which matrix is equal to $\begin{bmatrix}3&2\\-5&9end{bmatrix}$?\n$\begin{bmatrix}3&2&-5&9end{bmatrix}$\n$\begin{bmatrix}3&-5&2&9end{bmatrix}$\n$\begin{bmatrix}3&2\\-5&9end{bmatrix}$\n$\begin{bmatrix}3&-5\\2&9end{bmatrix}$

which matrix is equal to $\begin{bmatrix}3&2\\-5&9end{bmatrix}$?\n$\begin{bmatrix}3&2&-5&9end{bmatrix}$\n$\begin{bmatrix}3&-5&2&9end{bmatrix}$\n$\begin{bmatrix}3&2\\-5&9end{bmatrix}$\n$\begin{bmatrix}3&-5\\2&9end{bmatrix}$

Answer

Explanation:

Step1: Recall matrix equality

Two matrices are equal if they have the same dimensions and corresponding elements are equal. The given matrix $\begin{bmatrix}3&2\ - 5&9\end{bmatrix}$ is a $2\times2$ matrix (2 rows and 2 columns).

Step2: Analyze each option

  • Option 1: $\begin{bmatrix}3&2&-5&9\end{bmatrix}$ is a $1\times4$ matrix, not equal.
  • Option 2: $\begin{bmatrix}3&-5&2&9\end{bmatrix}$ is a $1\times4$ matrix, not equal.
  • Option 3: $\begin{bmatrix}3&2\ - 5&9\end{bmatrix}$ is a $2\times2$ matrix with elements matching the given matrix.
  • Option 4: $\begin{bmatrix}3&-5\2&9\end{bmatrix}$ has different element - order in rows, not equal.

Answer:

$\begin{bmatrix}3&2\ - 5&9\end{bmatrix}$ (the third option)