For Exercises 65-66, find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian elimination to find A, B, and C . 5 x 2 − 6 x − 13 ( x + 3 ) ( x − 2 ) 2 = A x + 3 + B x − 2 + C ( x − 2 ) 2
For Exercises 65-66, find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian elimination to find A, B, and C . 5 x 2 − 6 x − 13 ( x + 3 ) ( x − 2 ) 2 = A x + 3 + B x − 2 + C ( x − 2 ) 2
Solution Summary: The author explains how to solve a system of linear equations using Gaussian elimination.
For Exercises 65-66, find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian elimination to find A,B, and C.
5
x
2
−
6
x
−
13
(
x
+
3
)
(
x
−
2
)
2
=
A
x
+
3
+
B
x
−
2
+
C
(
x
−
2
)
2
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ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0.
y Af
-2
1
2 4x
a. The function is increasing when
and
decreasing when
By forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1
if a=2 and b=1
1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2
2)Find a matrix C such that (B − 2C)-1=A
3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)
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