Operations with Matrices

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form of rows x columns (e.g., 3x4 means 3 rows and 4 columns).

Front

Can you multiply a 2x3 matrix by a 3x12 matrix?

Back

Yes, you can multiply a 2x3 matrix by a 3x12 matrix because the number of columns in the first matrix (3) matches the number of rows in the second matrix (3).

Front

What is the result of subtracting two matrices A and B?

Back

The result of subtracting two matrices A and B is obtained by subtracting corresponding elements, provided both matrices have the same dimensions.

Front

What is the result of multiplying the following matrices: \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \) and \( \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)?

Back

The result is \( \begin{pmatrix} 2*5 + 3*7 & 2*6 + 3*8 \\ 1*5 + 4*7 & 1*6 + 4*8 \end{pmatrix} = \begin{pmatrix} 41 & 54 \\ 33 & 38 \end{pmatrix} \).

Front

What does it mean if two matrices cannot be added or subtracted?

Back

Two matrices cannot be added or subtracted if they do not have the same dimensions (i.e., the same number of 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. For example, the 2x2 identity matrix is \( \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \).

Front

What is the zero matrix?

Back

The zero matrix is a matrix in which all elements are zero. It can be of any size, such as \( \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \).

Front

How do you find the transpose of a matrix?

Back

The transpose of a matrix is found by swapping its rows and columns. For example, the transpose of \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is \( \begin{pmatrix} a & c \\ b & d \end{pmatrix} \).

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 multiplication of a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a constant number). For example, multiplying \( k \) by \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) results in \( \begin{pmatrix} ka & kb \\ kc & kd \end{pmatrix} \).