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. Both matrices must have the same dimensions.

Front

How do you subtract two matrices?

Back

To subtract two matrices, subtract their corresponding elements. Both 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

\[ \begin{pmatrix} 14 & 10 \\ -10 & -4 \end{pmatrix} \]

Front

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

Back

\[ \begin{pmatrix} 3 & -3 \\ 5 & -9 \end{pmatrix} \]

Front

What does it mean for matrices to be compatible for addition or subtraction?

Back

Matrices are compatible for addition or subtraction if they have the same dimensions (same number of rows and columns).

Front

How do you multiply two matrices?

Back

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting matrix has dimensions of the number of rows from the first matrix and the number of columns from the second matrix.

Front

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

Back

\[ \begin{pmatrix} -75 & -150 \\ 0 & -300 \end{pmatrix} \]

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all the elements are zero.

Front

What is the identity matrix?

Back

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.