Practical_11.19.24_Operations with Matrices

Front

What is the result of subtracting the matrix \( \begin{pmatrix} 3 & -4 \\ 8 & -13 \end{pmatrix} \) from \( \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \)?

Back

The result is \( \begin{pmatrix} -3 & 4 \\ -8 & 13 \end{pmatrix} \).

Front

What is the result of subtracting the matrix \( \begin{pmatrix} -9 \\ 8 \\ 3 \\ 2 \end{pmatrix} \) from \( \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} \)?

Back

The result is \( \begin{pmatrix} 9 \\ -8 \\ -3 \\ -2 \end{pmatrix} \).

Front

What does the expression \( 3A \) represent when \( A \) is a matrix?

Back

It represents the matrix obtained by multiplying each element of matrix \( A \) by 3.

Front

How many rows are in a 5 x 4 matrix?

Back

A 5 x 4 matrix has 5 rows.

Front

How do you multiply two matrices?

Back

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting matrix will have dimensions equal to the number of rows of the first matrix and the number of columns of the second matrix.

Front

What is the result of multiplying the matrices \( \begin{pmatrix} -4 & 5 \\ 6 & -2 \end{pmatrix} \) and \( \begin{pmatrix} 5 & 0 \\ 1 & 3 \end{pmatrix} \)?

Back

The result is \( \begin{pmatrix} -20 & 15 \\ 30 & -18 \end{pmatrix} \).

Front

What is the definition of a matrix?

Back

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

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 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 the transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns.