Determinants and Matrix Inverses

The video tutorial explains how to determine if 3x3 matrices are invertible by checking if they have an inverse. It introduces the concept of matrix invertibility, emphasizing that a matrix is invertible if its determinant is non-zero. Two methods for finding determinants are discussed: the diagonal method and the expansion by minors method. The tutorial provides a step-by-step guide to calculating the determinant of matrices A and C using these methods, concluding that matrix A is invertible while matrix C is not.

What is a necessary condition for a matrix to be invertible?

• It must be a diagonal matrix.

• It must have a zero determinant.

• It must be a square matrix.

• It must have all positive elements.

What does it mean if a matrix is non-singular?

• It has no inverse.

• It has a zero determinant.

• It is not a square matrix.

• It has an inverse.

Which method is NOT mentioned for finding the determinant of a matrix?

• Diagonal method

• Expansion by minors

• Gaussian elimination

• Method of co-actors

In the diagonal method, what is the first step to find the determinant?

• Find the inverse of the matrix.

• Transpose the matrix.

• Multiply all elements of the matrix.

• Copy down the elements of the first two columns.

What is the determinant of Matrix A calculated using the diagonal method?

• 15

• 4

• -4

• 0

What is the purpose of the expansion by minors method?

• To calculate the determinant of a matrix.

• To transpose a matrix.

• To find the inverse of a matrix.

• To solve linear equations.

Which row is used for the expansion by minors in the example?

• Third row

• Second row

• First row

• Any row

What is the determinant of Matrix C calculated using the expansion by minors?

• 0

• 13

• 1

• -4

What conclusion can be drawn if the determinant of a matrix is zero?

• The matrix is invertible.

• The matrix is non-singular.

• The matrix is singular.

• The matrix is a diagonal matrix.

What is another term used for a non-invertible matrix?

• Identity

• Diagonal

• Non-singular

• Singular