Introduction to Matrices - 5th

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers 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', indicating how many rows and columns it has.

Front

What must be true in order to ADD two matrices?

Back

The dimensions of the two matrices must be equal.

Front

What is the result of adding the matrices: \[ \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix} + \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \]?

Back

\[ \begin{bmatrix} 8 & 8 \\ 8 & 12 \end{bmatrix} \]

Front

What is the result of subtracting the matrices: \[ \begin{bmatrix} 5 & 7 \\ 9 & 2 \end{bmatrix} - \begin{bmatrix} 3 & 4 \\ 1 & 1 \end{bmatrix} \]?

Back

\[ \begin{bmatrix} 2 & 3 \\ 8 & 1 \end{bmatrix} \]

Front

What is the identity matrix?

Back

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

Front

What is a zero matrix?

Back

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

Front

Can you multiply two matrices of different dimensions?

Back

No, 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: \[ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \times \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \]?

Back

\[ \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix} \]

Front

What is a scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number).