Exercise 72 Page 227

To find the inverse of the given 2* 2 matrix, we will use the corresponding formula.

Matrix	Inverse
A= [ cc a & b c & d ]	A^(- 1)=1/ad-bc [ cc d & - b - c & a ] where ad-bc ≠ 0

The expression ad-bc is known as the determinant of a 2* 2 matrix. Because it is in the denominator of a fraction, if the determinant is zero, the matrix cannot have an inverse. Consider the given matrix. [ cc 2 & 8 - 3 & - 5 ] Let's calculate its determinant.

ad-bc

SubstituteValues

Substitute values

2(- 5)- 8( - 3)

▼

Simplify

MultPosNeg

a(- b)=- a * b

- 10-8(- 3)

MultNegNegOnePar

- a(- b)=a* b

- 10+24

AddTerms

Add terms

14

Since the determinant is not zero, the matrix has an inverse. We can now apply the formula for the inverse. Note that we usually refer to the determinant using the notation ad-bc=det(A).

1/det(A) d & - b - c & a

SubstituteValues

Substitute values

1/14 - 5 & - 8 3 & 2

Multiply matrix by 1/14

& 1/14 (- 5) & 1/14 (- 8) & & 1/14 (3) & 1/14 (2) &

Multiply

Multiply

& - 5/14 & & - 4/7 & & 3/14 & & 1/7 &