Matrix Operations Review

Front

What is the result of the matrix operation B - A if A = [[1, 2], [3, 4]] and B = [[4, 2], [7, 3]]?

Back

B - A = [[4-1, 2-2], [7-3, 3-4]] = [[3, 0], [4, -1]]

Front

How do you represent the system of equations -3x + 5y = 25 and 2x - 10y = -7 using matrices?

Back

The system can be represented as: \[ \begin{bmatrix} -3 & 5 \\ 2 & -10 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 25 \\ -7 \end{bmatrix} \]

Front

What are the dimensions of the resulting matrix when multiplying a 4x3 matrix by a 3x2 matrix?

Back

The resulting matrix will have dimensions 4x2.

Front

Can two matrices of dimensions 3x4 and 4x3 be multiplied?

Back

Yes, they can be multiplied because the number of columns in the first matrix (4) matches the number of rows in the second matrix (4).

Front

What is the condition for two matrices to be added together?

Back

Two matrices can be added if they have the same dimensions.

Front

If matrix A is 2x3 and matrix B is 3x2, what is the size of the product AB?

Back

The product AB will be a 2x2 matrix.

Front

What does it mean if the multiplication of two matrices is undefined?

Back

It means that the number of columns in the first matrix does not match the number of rows in the second matrix.

Front

If matrix A is 3x2 and matrix B is 2x3, what is the size of the resulting matrix when A is multiplied by B?

Back

The resulting matrix will be 3x3.

Front

What is the result of the operation if matrix A is 2x2 and matrix B is 2x3?

Back

The operation A + B is undefined because the matrices have different dimensions.

Front

What is the identity matrix for a 2x2 matrix?

Back

The identity matrix for a 2x2 matrix is \[ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]