# Worksheet: Scalar Multiplication of Matrices

In this worksheet, we will practice multiplying a scalar by a matrix and identifying the properties of their multiplication.

Q1:

Given the matrix what is ?

• A
• B
• C
• D
• E

Q2:

Find numbers , , and so that .

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q3:

Given that find the value of .

Q4:

Let be a matrix whose entries are all zero. If is any matrix, which of following is equivalent to ?

• A
• B
• C
• D
• E

Q5:

Given the matrix what is the greatest number for which no entry of is greater than 1?

• A
• B
• C
• D
• E

Q6:

If , what is ?

• A
• B
• C
• D6
• E

Q7:

Consider the matrix . Find .

• A
• B
• C
• D

Q8:

If , what is ?

• A
• B
• C
• D
• E0

Q9:

Olivia has defined the notion of a 'prime matrix' as follows. A matrix is a prime matrix if the following two conditions hold:

1. It is none zeros with integers entries.
2. If , then or .

Which of the following matrices are prime according to Olivia's definition?

• A
• B
• C
• D
• E

Q10:

Consider the matrix equation Find the value of that solves this equation.