Question

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

A constant by which you multiply a matrix is called a scalar.

Short answer

The given statement is true.

Step-by-step solution

Step 1. Define the concept of scalar multiplication.

The product of a scalar k and an$m\times n$ matrix is an$m\times n$ matrix in which each element equals k times the corresponding elements of the original matrix.

Step 2. Explanation of the statement.

As per the statement, a constant by which you multiply a matrix is called a scalar and since, the product of the real numbers and a matrix is termed as scalar multiplication. In the scalar multiplication, the given scalar is used to multiply each entry of the matrix.

Step 3. State whether the statement is true or false.

The given statement “A constant by which you multiply a matrix is called a scalar.” is true.