Matrix Determinants and Cofactors

The video tutorial explains how to find the cofactor matrix of a given 2x2 matrix and then determine its adjoint by transposing the cofactor matrix. It covers the calculation of each cofactor by eliminating specific rows and columns, computing determinants, and assembling the cofactor matrix. Finally, it demonstrates how to transpose the cofactor matrix to obtain the adjoint.

What is the adjoint of a matrix in relation to its cofactor matrix?

• The square of the cofactor matrix

• The inverse of the cofactor matrix

• The transpose of the cofactor matrix

• The determinant of the cofactor matrix

How is the cofactor a11 calculated for a 2x2 matrix?

• By eliminating row 1 and column 2

• By eliminating row 1 and column 1

• By eliminating row 2 and column 1

• By eliminating row 2 and column 2

What is the determinant of a 1x1 matrix with an entry of 7?

• 7

• 1

• 49

• 0

What is the sign of the cofactor a12?

• Positive

• Negative

• Undefined

• Zero

Which entry is used to calculate the cofactor a12?

• Entry -2

• Entry 7

• Entry 3

• Entry 4

What is the result of multiplying negative one by negative two?

• 2

• 4

• 0

• -2

What is the determinant of a 1x1 matrix with an entry of 4?

• 4

• 3

• 2

• 1

What are the elements of the first row in the cofactor matrix?

• -3, 7

• 2, 4

• 4, 2

• 7, -3

How is the adjoint of a matrix formed from the cofactor matrix?

• By adding the rows

• By multiplying the matrix by 2

• By subtracting the columns

• By transposing the matrix

What is the second row of the adjoint matrix?

• 7, 2

• 2, 4

• -3, 4

• 4, -3