Matrix Inverses and Determinants

The video tutorial covers the basics of a 2x2 matrix, including its elements and how to find its inverse using the determinant and adjoint. It explains the conditions under which a matrix is non-invertible, specifically when the determinant is zero. The tutorial also provides examples to illustrate how to determine if a matrix is invertible or not.

What is the formula for the inverse of a 2x2 matrix?

• 1 over the determinant times the adjoint

• Determinant times the adjoint

• Determinant divided by the adjoint

• 1 over the adjoint times the determinant

What makes a matrix non-invertible?

• The adjoint is zero

• The elements are negative

• The determinant is zero

• The matrix is not square

If the determinant of a matrix is zero, what does it imply?

• The matrix is singular

• The matrix is diagonal

• The matrix is non-invertible

• The matrix is invertible

What is the condition for a 2x2 matrix to have a zero determinant?

• a*b = c*d

• a*d = c*b

• a*d = b*c

• a*c = b*d

In a non-invertible matrix, what is the relationship between a/b and c/d?

• a/b > c/d

• a/b ≠ c/d

• a/b < c/d

• a/b = c/d

For the matrix [5, 1; 3, 2], what is the determinant?

• 5

• 7

• 0

• 10

Is the matrix [5, 1; 3, 2] invertible?

• Only if a = b

• No

• Only if c = d

• Yes

For the matrix [10, 20; 250, 500], what is the determinant?

• 10000

• 5000

• 2500

• 0

Is the matrix [10, 20; 250, 500] invertible?

• No

• Only if b = d

• Yes

• Only if a = c

What happens if you try to find the inverse of a matrix with a zero determinant?

• It is one

• It is infinite

• It is zero

• It is undefined