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.

Tags

CCSS.HSA.REI.C.9

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.

Tags

CCSS.HSA.REI.C.9

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

• Identity

• Diagonal

• Non-singular

• Singular

Tags

CCSS.HSA.REI.C.9