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If A = [[1, 2], [3, 4]], what is A^2?
If A = [[1, 2], [3, 4]], what is A^2?
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Practice Questions
1 question
Q1
If A = [[1, 2], [3, 4]], what is A^2?
[7, 10; 15, 22]
[1, 2; 3, 4]
[10, 14; 22, 30]
[-1, -2; -3, -4]
Show Solution
Copy
A^2 = A * A = [[1*1 + 2*3, 1*2 + 2*4], [3*1 + 4*3, 3*2 + 4*4]] = [[7, 10], [15, 22]].
Questions & Step-by-step Solutions
1 item
Q
Q: If A = [[1, 2], [3, 4]], what is A^2?
Solution:
A^2 = A * A = [[1*1 + 2*3, 1*2 + 2*4], [3*1 + 4*3, 3*2 + 4*4]] = [[7, 10], [15, 22]].
Steps: 8
Show Steps
Step 1: Understand that A^2 means A multiplied by itself, which is A * A.
Step 2: Write down the matrix A: A = [[1, 2], [3, 4]].
Step 3: Set up the multiplication of A by itself: A * A = [[1, 2], [3, 4]] * [[1, 2], [3, 4]].
Step 4: Calculate the first element of the resulting matrix: (1*1 + 2*3) = 1 + 6 = 7.
Step 5: Calculate the second element of the first row: (1*2 + 2*4) = 2 + 8 = 10.
Step 6: Calculate the first element of the second row: (3*1 + 4*3) = 3 + 12 = 15.
Step 7: Calculate the second element of the second row: (3*2 + 4*4) = 6 + 16 = 22.
Step 8: Combine all the calculated elements into the resulting matrix: A^2 = [[7, 10], [15, 22]].
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