Matrix Inversion Using the Adjoint Method

The video tutorial explains how to find the inverse of a matrix using the adjoint method. It starts by discussing the determinant and co-actor matrix of matrix B. The adjoint method is introduced, which involves transposing the co-actor matrix to find the adjoint. The tutorial then demonstrates how to calculate the transpose and adjoint of matrix B. Finally, it shows the process of finding B inverse by multiplying the adjoint by the reciprocal of the determinant and simplifying the resulting matrix.

What is the determinant of Matrix B given in the problem?

• 49

• 81

• 64

• 100

Which method is used to find the inverse of Matrix B?

• QR Decomposition

• Gaussian Elimination

• Adjoint Method

• LU Decomposition

What is the first step in finding the adjoint of Matrix B?

• Multiply by the determinant

• Transpose the co-actor matrix

• Use row reduction

• Find the inverse directly

How is the adjoint of a matrix related to its co-actor matrix?

• It is the inverse of the co-actor matrix

• It is the square of the co-actor matrix

• It is the transpose of the co-actor matrix

• It is the determinant of the co-actor matrix

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

• Inverse = Adjoint / Determinant

• Inverse = 1 / Determinant * Adjoint

• Inverse = Determinant * Adjoint

• Inverse = Adjoint * Determinant

What is the simplified form of 27/81 in the inverse matrix?

• 1/2

• 3/4

• 2/3

• 1/3

What is the simplified form of 54/81 in the inverse matrix?

• 3/4

• 2/3

• 1/3

• 1/2

In the inverse matrix, what is the value in the second row, first column?

• 1/3

• -1/3

• 0

• -1

What is the value in the fourth row, second column of the inverse matrix?

• 0

• -1

• 1/3

• 1

What is the common form of presenting the inverse matrix?

• In decimal form

• As a percentage

• As a single fraction

• In simplified fraction form