Question

You combined matrices in various ways using matrix operations. Given the matrices below, choose the correct answer for each statement:

A = [ 1 2 4 ]
[ -5 8 9 ]
B = [ 0,5 0,7 ]
[ 0,9 0,1 ]
[ 4 ]
C = [ 3 ]
[-6]
D = [ 1/2 1 ]
[ 0 -1/3]

The following matrices can be multiplied together:____

Answer 1

The matrices that can be multiplied together from the given options are A and B, resulting in a 2x2 matrix, and A and C, resulting in a 2x1 matrix. Matrix multiplication is not commutative, meaning the order of multiplication matters and not all pairs can be multiplied.

Step-by-step explanation:

The question asks about combining matrices using various matrix operations. To determine which matrices can be multiplied together, we need to consider the dimensions of each matrix and the rules of matrix multiplication. The rule is that if matrix A has dimensions m x n and matrix B has dimensions p x q, we can multiply A by B only if n equals p, resulting in a new matrix with dimensions m x q.

Looking at the provided matrices:

• Matrix A is a 2x3 matrix.
• Matrix B is a 3x2 matrix.
• Matrix C is a 3x1 matrix.
• Matrix D is a 2x2 matrix.

Based on these dimensions, the following matrix multiplications are possible:

1. A can be multiplied by B (2x3 multiplied by 3x2), resulting in a 2x2 matrix.
2. A can be multiplied by C (2x3 multiplied by 3x1), resulting in a 2x1 matrix.
3. D can be multiplied by A (2x2 multiplied by 2x3) is not possible since the number of columns in D is not equal to the number of rows in A.

Therefore, the matrices that can be multiplied together according to the given list are A and B, as well as A and C.

It's important to note that the commutative property does not hold for matrix multiplication; that is, AB does not necessarily equal BA.

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