Scalar Multiplication of Matrices

What is the definition of scalar multiplication of matrices?

• Scalar multiplication is the process of finding the determinant of a matrix

• Scalar multiplication of matrices is the process of multiplying each element of a matrix by a scalar (a single number).

• Scalar multiplication is the process of adding two matrices together

• Scalar multiplication is the process of dividing each element of a matrix by a scalar

True or False: Scalar multiplication of matrices is commutative.

• Sometimes

• Depends

• True

• False

What is the result of scalar multiplication: -5 * [[1, 2], [3, 4]]?

• [[-5, 10], [15, -20]]

• [[-1, -2], [-3, -4]]

• [[5, 10], [15, 20]]

• [[-5, -10], [-15, -20]]

Which property of scalar multiplication states that the product of a scalar and a matrix is equal to the product of the scalar and each element of the matrix?

• Associative property

• Distributive property

• Commutative property

• Identity property

Calculate the scalar multiplication: 2 * [[-1, 3], [2, -4]] = ?

• [[3, -1], [-4, 2]]

• [[-2, 6], [4, -8]]

• [[-3, 1], [4, -2]]

• [[2, -6], [-4, 8]]

What is the result of scalar multiplication: 0 * [5, -2, 7]?

• [5, -2, 7]

• [0, 0, 0]

• [0, 5, -2, 7]

• [0, 0, 5, -2, 7]

Which property of scalar multiplication states that the product of two scalars and a matrix is equal to the product of the scalars and the matrix?

• Commutative property

• Associative property

• Identity property

• Distributive property

Provide an example of an application of scalar multiplication in real life.

• Using scalar multiplication to divide the size of a room in half

• An example of scalar multiplication in real life is when a farmer increases the size of their crop field by multiplying the original dimensions by a scalar value, such as doubling the length and width to increase the overall area.

• Applying scalar multiplication to increase the speed of a car

• Using scalar multiplication to decrease the amount of ingredients in a recipe