11
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Scalar and Matrix Multiplication

Question 11 • GA-Advanced Algebra: Concepts and Connections CR

Which of the following statements are true about scalar multiplication of matrices?

Answer
A
You can multiply a matrix of any size by a scalar.
B
For any matrix A, 1 × A = A.
C
For any scalar r, rI = I, where I is the identity matrix.
D
You can scale geometric figures using scalar multiplication.
E
Scalar multiplication is a shortcut for repeated addition of the same matrix.
F
Scalar multiplication is not possible for matrices that are not square.

Explanation

A scalar can multiply a matrix of any dimensions: multiply each entry by that scalar. Multiplying by 1 leaves every entry unchanged, so 1 × A = A. Scalar multiplication can also scale the coordinates of geometric figures, and for a positive whole-number scalar it is equivalent to adding the matrix to itself that many times. C is false because rI equals I only when r = 1; F is false because matrices do not have to be square.

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