9(z− 1)
^2 + 12 (z − 1) + 4
Answers
Answer:
Explanation:
x
2
−
7
x
−
5
=
0
Quadratic formula is
x
=
−
b
±
√
b
2
−
4
a
c
2
a
Values given
a
=
1
,
b
=
−
7
,
c
=
−
5
x
=
−
(
−
7
)
±
√
(
−
7
)
2
−
4
×
1
×
(
−
5
)
2
×
1
x
=
7
±
√
49
+
20
2
x
=
7
±
√
69
2
x
=
7
+
√
69
2
and
x
=
7
−
√
69
2
∴
x
=
7.65
and
x
=
−
0.65
Answer:
Solving a System of Linear Equations Using Matrices
We have seen how to write a system of equations with an augmented matrix, and then how to use row operations and back-substitution to obtain row-echelon form. Now, we will take row-echelon form a step farther to solve a 3 by 3 system of linear equations. The general idea is to eliminate all but one variable using row operations and then back-substitute to solve for the other variables.
EXAMPLE 6: SOLVING A SYSTEM OF LINEAR EQUATIONS USING MATRICES
Solve the system of linear equations using matrice.
9
SOLUTION
First, we write the augmen
⎦
Next, we perform row operations to obtain row-echelon form.
The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R
2
and \displaystyle {R}_{3}R
3
.
Interchange
The last matrix represents the equivalent system
1
Using back-substitution, we obtain the solution as \displaystyle \left(4,-3,1\right)(4,−3,1).