Perform the matrix multiplication: [2 3; 4 5] * [1 0; 0 1]. a. [2 3; 4 5] b. [3 2; 5 4] c. [2 3; 5 6] d. [2 0; 0 5]
Question
Perform the matrix multiplication: [2 3; 4 5] * [1 0; 0 1].
a. [2 3; 4 5]
b. [3 2; 5 4]
c. [2 3; 5 6]
d. [2 0; 0 5]
Solution
The multiplication of the given matrices [2 3; 4 5] * [1 0; 0 1] is performed as follows:
First, we multiply the first row of the first matrix by the first column of the second matrix:
(21) + (30) = 2
Then, we multiply the first row of the first matrix by the second column of the second matrix:
(20) + (31) = 3
Next, we multiply the second row of the first matrix by the first column of the second matrix:
(41) + (50) = 4
Finally, we multiply the second row of the first matrix by the second column of the second matrix:
(40) + (51) = 5
So, the result of the matrix multiplication is [2 3; 4 5], which corresponds to option (a).
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