Intro to Matrices and Operations with Matrices

Front

What is a Matrix?

Back

A set of numbers arranged in rows and columns.

Front

What must be true in order to ADD two matrices?

Back

The dimensions of the matrices must be equal.

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: \( \begin{pmatrix} 10 & -9 \\ 8 & 3 \end{pmatrix} - \begin{pmatrix} 5 & -8 \\ 3 & 2 \end{pmatrix} \)?

Back

\( \begin{pmatrix} 5 & -1 \\ 5 & 1 \end{pmatrix} \)

Front

What is the determinant of a 2x2 matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \)?

Back

The determinant is calculated as \( ad - bc \).

Front

What is a scalar in relation to matrices?

Back

A scalar is a single number that can multiply a matrix.

Front

What is the identity matrix for 2x2 matrices?

Back

The identity matrix is \( \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \).

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 a matrix by a scalar?

Back

Each element of the matrix is multiplied by the scalar.

Front

What is the zero matrix?

Back

A matrix in which all elements are zero.