Matrix Inverses and Determinants

The video tutorial explains how to determine if a 3x3 matrix is invertible by calculating its determinant. It covers the conditions under which a matrix is invertible, the process of calculating the determinant using cofactor expansion, and solving for a specific variable, H, that makes the matrix non-invertible. The tutorial concludes by confirming that there is only one value of H that satisfies this condition.

What condition must be met for a matrix to be considered non-invertible?

• The matrix must have a column of ones.

• The matrix must have a row of zeros.

• The determinant must be zero.

• The matrix must be square.

What is the first step in calculating the determinant of a 3x3 matrix?

• Select any row or column for expansion.

• Multiply all diagonal elements.

• Add all elements of the matrix.

• Subtract the sum of the first row from the last row.

Which row is used for the determinant calculation in the given example?

• Row three

• Row two

• Row one

• Column one

What is the determinant of the 2x2 matrix formed after deleting row three and column one?

• 12

• 15

• 9

• 3

What is the result of simplifying the expression 7 times (12 - 15)?

• 3

• 21

• -21

• 0

What is the value of H that makes the determinant zero?

• H = 12

• H = 6

• H = 3

• H = 9

What happens if H is not equal to 9 in the given matrix?

• The matrix becomes diagonal.

• The matrix becomes invertible.

• The matrix becomes symmetric.

• The matrix becomes singular.

What is the significance of the determinant being zero for the matrix?

• The matrix is singular.

• The matrix is orthogonal.

• The matrix is non-invertible.

• The matrix is invertible.

How many unique solutions exist for H in this problem?

• Infinitely many

• Two

• One

• None

What does it mean for a matrix to have an inverse?

• It can be added to another matrix to get a zero matrix.

• It can be multiplied by its inverse to get the identity matrix.

• It can be subtracted from another matrix to get the identity matrix.

• It can be multiplied by another matrix to get a zero matrix.