Scalar Multiplication of Matrices

Front

What is scalar multiplication of a matrix?

Back

Scalar multiplication of a matrix involves multiplying each element of the matrix by a scalar (a constant number).

Front

If A is a matrix and k is a scalar, what is the result of kA?

Back

The result of kA is a new matrix where each element of matrix A is multiplied by the scalar k.

Front

How does scalar multiplication affect the size of a matrix?

Back

Scalar multiplication does not change the size (dimensions) of the matrix; it only changes the values of its elements.

Front

What is the effect of multiplying a matrix by zero?

Back

Multiplying any matrix by zero results in a zero matrix of the same dimensions.

Front

If A = [[1, 2], [3, 4]] and k = 3, what is kA?

Back

kA = [[3*1, 3*2], [3*3, 3*4]] = [[3, 6], [9, 12]].

Front

What happens when a matrix is multiplied by -1?

Back

Multiplying a matrix by -1 changes the sign of each element in the matrix.

Front

Can scalar multiplication be applied to non-square matrices?

Back

Yes, scalar multiplication can be applied to any matrix, regardless of whether it is square or non-square.

Front

If A = [[2, 4], [6, 8]] and k = 0.5, what is kA?

Back

kA = [[0.5*2, 0.5*4], [0.5*6, 0.5*8]] = [[1, 2], [3, 4]].

Front

What is the identity property of scalar multiplication?

Back

The identity property states that multiplying a matrix by 1 leaves the matrix unchanged.

Front

If A = [[5, 10], [15, 20]] and k = -2, what is kA?

Back

kA = [[-2*5, -2*10], [-2*15, -2*20]] = [[-10, -20], [-30, -40]].