Exercise 70 Page 970

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 & 1 4 & - 1 ] Let's calculate its determinant.

ad-bc

SubstituteValues

Substitute values

- 2( - 1)- 1( 4)

▼

Simplify

MultNegNegOnePar

- a(- b)=a* b

2-1(4)

Multiply

Multiply

2-4

SubTerm

Subtract term

- 2

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/- 2 - 1 & - 1 - 4 & - 2

MoveNegDenomToFrac

Put minus sign in front of fraction

- 1/2 - 1 & - 1 - 4 & - 2

Multiply matrix by - 1/2

& - 1/2 (- 1) & - 1/2 (- 1) & & - 1/2 (- 4) & - 1/2 (- 2) &

MultNegNegOnePar

- a(- b)=a* b

& 1/2 & 1/2 & & 4/2 & 2/2 &

CalcQuot

Calculate quotient

& 1/2 & 1/2 & & 2 & 2/2 &

QuotOne

a/a=1

& 1/2 & 1/2 & & 2 & 1 &

Rewrite

Rewrite 1/2 as 0.5

& 0.5 & 0.5 & & 2 & 1 &

This corresponds to option G.