Multiplying Matrices

Front

What is scalar multiplication in matrices?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number). For example, if matrix A = [[1, 2], [3, 4]] and the scalar is 2, then 2A = [[2, 4], [6, 8]].

Front

When can two matrices be multiplied?

Back

Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Front

What is the dimension of the product of two matrices A (1x4) and B (4x7)?

Back

The dimension of the product AB is 1x7.

Front

If matrix A is 4x2 and matrix B is 3x3, can they be multiplied?

Back

No, they cannot be multiplied because the number of columns in A (2) does not equal the number of rows in B (3).

Front

What is the result of multiplying a 2x3 matrix by a 3x2 matrix?

Back

The result will be a 2x2 matrix.

Front

Define the term '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. For example, the 2x2 identity matrix is [[1, 0], [0, 1]].

Front

What is the zero matrix?

Back

The zero matrix is a matrix in which all elements are zero. For example, a 2x2 zero matrix is [[0, 0], [0, 0]].

Front

How do you find the determinant of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is ad - bc.

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns. For example, the transpose of [[1, 2], [3, 4]] is [[1, 3], [2, 4]].