Inverse Matrix Operations and Verification

This video tutorial explains how to find the inverse of a 3x3 matrix using elementary row operations. It begins with setting up the problem and forming an augmented matrix. The tutorial then demonstrates step-by-step row operations to transform the matrix into its inverse. Finally, it verifies the result by multiplying the original matrix with its inverse to confirm it yields the identity matrix.

What is the first step in finding the inverse of a 3x3 matrix?

• Multiply the matrix by its transpose

• Set up an augmented matrix with the identity matrix

• Add all the elements of the matrix

• Transpose the matrix

Which operation is used to make the first element of the third row zero?

• Add Row 1 to Row 3

• Subtract Row 3 from Row 1

• Subtract Row 1 from Row 3

• Multiply Row 3 by a scalar

How do you transform a negative number in the second row to zero?

• Add Row 2 to Row 3

• Subtract Row 3 from Row 2

• Multiply Row 2 by a scalar

• Add a multiple of Row 1 to Row 2

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CCSS.HSA.REI.C.6

What is the purpose of multiplying Row 2 by 3 and subtracting 4 times Row 3?

• To make the second element of Row 3 zero

• To make the third element of Row 2 zero

• To make the first element of Row 2 zero

• To make the second element of Row 2 zero

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CCSS.HSN.VM.C.8

What is the result of adding Row 1 and Row 3?

• A new Row 1

• A new Row 2

• A new Row 3

• The identity matrix

What operation is performed to finalize the inverse matrix?

• Multiply the first row by 1/2 and the second row by 1/4

• Add Row 1 to Row 2

• Subtract Row 2 from Row 1

• Multiply the third row by 1/3

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CCSS.HSA.REI.C.9

How do you verify that the calculated matrix is indeed the inverse?

• By multiplying the original matrix with the calculated inverse

• By adding the original matrix to the calculated inverse

• By transposing the calculated inverse

• By checking if the determinant is zero

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What should the product of the original matrix and its inverse equal?

• A matrix with all elements equal to one

• The original matrix

• The identity matrix

• A zero matrix

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CCSS.HSN.VM.C.8

What is the result of multiplying the first row of the original matrix by the first column of the inverse?

• Zero

• Two

• Negative one

• One

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CCSS.HSA.REI.C.9

What is the final step in confirming the inverse matrix?

• Transpose the inverse matrix

• Check if the product with the original matrix is the identity matrix

• Multiply the inverse by a scalar

• Subtract the inverse from the original matrix

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CCSS.HSA.REI.C.9