6-1 Add/Subtract/Scalar Multiplication/Dimensions of Matrices

Front

What is the result of adding the following 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 are the dimensions of a matrix with 3 rows and 2 columns?

Back

3 x 2

Front

What does the entry \( a_{5,3} \) represent in a matrix?

Back

It represents the element located in the 5th row and 3rd column of the matrix.

Front

How many rows are in a 5 x 4 matrix?

Back

5

Front

What is the result of subtracting the following matrices? \[ \begin{pmatrix} -5 & -8 & 3 & 10 \end{pmatrix} - \begin{pmatrix} -9 & 8 & 3 & 2 \end{pmatrix} \]

Back

\[ \begin{pmatrix} 4 & -16 & 0 & 8 \end{pmatrix} \]

Front

Define scalar multiplication in the context of matrices.

Back

Scalar multiplication involves multiplying each entry of a matrix by a constant (scalar).

Front

What is the result of multiplying the matrix \[ \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} \] by the scalar 3?

Back

\[ \begin{pmatrix} 6 & 9 \\ 12 & 15 \end{pmatrix} \]

Front

If a matrix has dimensions 2 x 3, how many elements does it contain?

Back

It contains 6 elements.

Front

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

Back

\[ \begin{pmatrix} 6 & 8 \\ 10 & 12 \end{pmatrix} \]

Front

What is the definition of a matrix?

Back

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