AR Do Now - Matrices 12-10-24

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

How do you add two matrices?

Back

To add two matrices, add their corresponding elements. The matrices must have the same dimensions.

Front

What is the result of adding the matrices: \( \begin{pmatrix} 11 & 8 \\ -4 & 2 \end{pmatrix} + \begin{pmatrix} 3 & 2 \\ -6 & -6 \end{pmatrix} \)?

Back

The result is \( \begin{pmatrix} 14 & 10 \\ -10 & -4 \end{pmatrix} \).

Front

What does A - B represent in matrix operations?

Back

A - B represents the matrix obtained by subtracting matrix B from matrix A, done element-wise.

Front

What is the condition for subtracting two matrices?

Back

Both matrices must have the same dimensions (same number of rows and columns).

Front

How do you subtract two matrices?

Back

To subtract two matrices, subtract their corresponding elements.

Front

What is the result of subtracting the matrices: \( \begin{pmatrix} 3 & -8 \\ 0 & -1 \end{pmatrix} - \begin{pmatrix} 3 & -4 \\ 8 & -13 \end{pmatrix} \)?

Back

The result is \( \begin{pmatrix} 0 & -4 \\ -8 & 12 \end{pmatrix} \).

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix.

Front

What is the condition for multiplying two matrices?

Back

The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What is the result of multiplying the matrices: \( \begin{pmatrix} 20 & 15 \\ -10 & 30 \end{pmatrix} \times \begin{pmatrix} 1 & 0 \\ 0 & -5 \end{pmatrix} \)?

Back

The result is \( \begin{pmatrix} 20 & -75 \\ -10 & -150 \end{pmatrix} \).