Matrix Inversion Using the Adjoint Method

The video tutorial explains how to use the adjoint method to find the inverse of a matrix. It begins with an introduction to the adjoint method, followed by a detailed process of calculating the determinant of a matrix. The tutorial then covers the steps to find the cofactor matrix and concludes with the calculation of the adjoint and inverse of the matrix. The tutorial also includes a verification step using a matrix calculator.

What is the formula for finding the inverse of a matrix using the adjoint method?

• A inverse is equal to the determinant of A divided by the adjoint of A

• A inverse is equal to 1 divided by the determinant of A times the adjoint of A

• A inverse is equal to the transpose of A times the determinant of A

• A inverse is equal to the adjoint of A times the determinant of A

What is the determinant of the given 2x2 matrix?

• 22

• 20

• 17

• 15

How is the cofactor of an element in a matrix calculated?

• By adding the element to the sum of its row and column indices

• By subtracting the element from the sum of its row and column indices

• By raising -1 to the power of the sum of its indices and multiplying by the minor

• By multiplying the element by its row and column indices

What is the cofactor of the element in the first row and first column of the matrix?

• -1

• 5

• 1

• -5

What is the cofactor of the element in the second row and second column of the matrix?

• -3

• 3

• -2

• 2

How is the adjoint of a matrix formed?

• By inverting the cofactor matrix

• By adding the cofactor matrix to the original matrix

• By multiplying the cofactor matrix by the determinant

• By transposing the cofactor matrix

What is the first row of the adjoint matrix?

• [-1, -5]

• [-5, 2]

• [2, -5]

• [-5, -1]

What is the inverse of the matrix when the determinant is 17?

• 1/17 times the adjoint of A

• 17 times the adjoint of A

• 17 times the transpose of A

• 1/17 times the transpose of A

What is the value of the element in the first row and first column of the inverse matrix?

• -5/17

• 5/17

• -1/17

• 1/17

How can the inverse of a matrix be verified using a calculator?

• By entering the matrix and checking if the product with its inverse is the identity matrix

• By entering the matrix and checking if the product with its inverse is zero

• By entering the matrix and checking if the sum with its inverse is the identity matrix

• By entering the matrix and checking if the sum with its inverse is zero