Matrix Review

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'rows x columns'. For example, a matrix with 3 rows and 2 columns is said to have dimensions 3 x 2.

Front

How do you add two matrices?

Back

To add two matrices, they must have the same dimensions. Add corresponding elements from each matrix.

Front

What is the result of adding the matrices: \[ \begin{bmatrix} 11 & 8 \\ -4 & 2 \end{bmatrix} + \begin{bmatrix} 3 & 2 \\ -6 & -6 \end{bmatrix} \]?

Back

The result is \[ \begin{bmatrix} 14 & 10 \\ -10 & -4 \end{bmatrix} \].

Front

How do you subtract two matrices?

Back

To subtract two matrices, they must have the same dimensions. Subtract corresponding elements from the second matrix from the first.

Front

What is the result of subtracting the matrices: \[ \begin{bmatrix} -5 \\ 10 \end{bmatrix} - \begin{bmatrix} -9 \\ 8 \end{bmatrix} \]?

Back

The result is \[ \begin{bmatrix} 4 \\ 2 \end{bmatrix} \].

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. For example, \[ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \].

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero. For example, \[ Z = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix} \].

Front

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

Back

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

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns. For example, the transpose of \[ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \] is \[ A^T = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} \].