3.
Step 1: Choose a row or column Let’s choose the first row
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*Always remember that signs alternate. This will make more sense later.
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Step 2: Take the first number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers So we get 2 times the determinant of the matrix of non-circled numbers
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Step 2: Take the first number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers So we get 2 times the determinant of the matrix of the numbers in the rectangle
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Step 2: Take the first number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers 2*[(-5*6)-(8*0)] = 2*(-30-0) = -60
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Step 2: Take the first number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers 2*[(-5*6)-(8*0)] = 2*(-30-0) = -60 THIS IS NOT THE FINAL ANSWER!
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Step 3: Take the next number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers This is where the alternating signs come in
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This is where the alternating signs come in Since the circled number is in the same position as a negative sign, we multiply it by negative 1 before multiplying it by the determinant of the 2x2 matrix in Step 4
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Step 3: Take the next number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers -(-3)*[(5*-5)-(8*1)] = 3*(-25-8) = -99
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Step 3: Take the next number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers -(-3)*[(5*-5)-(8*1)] = 3*(-25-8) = -99 THIS IS NOT THE FINAL ANSWER!
13.
Step 4: Take the last number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers 11*[(5*0)-(6*1) = 11*(0-6) = -66
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Step 4: Take the last number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers 11*[(5*0)-(6*1) = 11*(0-6) = -66 THIS IS NOT THE FINAL ANSWER!
15.
We now have the three parts of our answer. To find the actual answer, we take the sum of our three parts -60 -99 -66 = -225 So the determinant of our matrix is -225
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