Matrices Test (for an accuracy grade)

Front

What are the dimensions of a matrix with 3 rows and 2 columns?

Back

3 x 2

Front

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

Back

\[ \begin{bmatrix} -15 & 1 & -5 \end{bmatrix} \]

Front

What does it mean if a matrix A is singular?

Back

A matrix A is singular if its determinant is zero, meaning it does not have an inverse (A^-1 does not exist).

Front

What are the dimensions of a matrix with 3 rows and 1 column?

Back

3 x 1

Front

Which matrix can a 2 x 3 matrix be multiplied by?

Back

A 2 x 3 matrix can be multiplied by a 3 x n matrix, where n can be any positive integer.

Front

What is the result of multiplying a 2 x 3 matrix by a 3 x 2 matrix?

Back

The result is a 2 x 2 matrix.

Front

What is the identity matrix of size 3 x 3?

Back

The identity matrix of size 3 x 3 is \[ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \].

Front

How do you find the determinant of a 2 x 2 matrix \[ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \]?

Back

The determinant is calculated as ad - bc.

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by flipping it over its diagonal, switching the row and column indices.

Front

What is the result of adding two matrices of the same dimensions?

Back

The result is a matrix of the same dimensions where each element is the sum of the corresponding elements.