If A = [[2, 3], [1, 4]], what is A^2? (2020)

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Question: If A = [[2, 3], [1, 4]], what is A^2? (2020)

Options:

Correct Answer: [[12, 21], [21, 16]]

Exam Year: 2020

Solution:

A^2 = A * A = [[2*2 + 3*1, 2*3 + 3*4], [1*2 + 4*1, 1*3 + 4*4]] = [[10, 21], [21, 16]].

If A = [[2, 3], [1, 4]], what is A^2? (2020)

If A = [[2, 3], [1, 4]], what is A^2? (2020)

Step 1: Understand that A^2 means we need to multiply matrix A by itself.
Step 2: Write down matrix A: A = [[2, 3], [1, 4]].
Step 3: Set up the multiplication of A * A. This means we will calculate each element of the resulting matrix.
Step 4: Calculate the element in the first row and first column of the result: 2*2 + 3*1 = 4 + 3 = 7.
Step 5: Calculate the element in the first row and second column of the result: 2*3 + 3*4 = 6 + 12 = 18.
Step 6: Calculate the element in the second row and first column of the result: 1*2 + 4*1 = 2 + 4 = 6.
Step 7: Calculate the element in the second row and second column of the result: 1*3 + 4*4 = 3 + 16 = 19.
Step 8: Combine all the calculated elements into the resulting matrix: A^2 = [[7, 18], [6, 19]].

Matrix Multiplication – Understanding how to multiply matrices, including the rules for combining elements from rows and columns.
Matrix Squaring – Applying matrix multiplication to find the square of a matrix, which involves multiplying the matrix by itself.