Consider the following two systems. (a) -5х — у 1 4x + 5y -1 (b) (-5x – y 3 4x + 5y -2 (i) Find the inverse of the (common) coefficient matrix of the two systems. A-1 = (ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A-B where B represents the right hand side (i.e. B = for system (a) and B = for system (b). Solution to system (a): x = Solution to system (b): a =
Consider the following two systems. (a) -5х — у 1 4x + 5y -1 (b) (-5x – y 3 4x + 5y -2 (i) Find the inverse of the (common) coefficient matrix of the two systems. A-1 = (ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A-B where B represents the right hand side (i.e. B = for system (a) and B = for system (b). Solution to system (a): x = Solution to system (b): a =
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 83E: Explain the difference between the row-echelon form and the reduced row-echelon form of a matrix.
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Consider the following two systems.
(a)
{−5x−y4x+5y==1−1{−5x−y=14x+5y=−1
(b)
{−5x−y4x+5y==3−2{−5x−y=34x+5y=−2
(i) Find the inverse of the (common) coefficient matrix of the two systems.
| A−1=A−1= |
|
(ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A−1BA−1B where BB represents the right hand side (i.e. B=[1−1]B=[1−1] for system (a) and B=[3−2]B=[3−2] for system (b)).
Solution to system (a): x=x= , yy =
Solution to system (b): x=x= , yy =
Transcribed Image Text:Consider the following two systems.
(a)
-5x
1
4х + 5y
-1
(b)
{
-5x – Y
4а + 5y
(i) Find the inverse of the (common) coefficient matrix of the two systems.
A-1
(ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A-'B where B represents the right hand side (i.e. B
1
for system (a) and B
3
for system (b)).
Solution to system (a): x =
· Y =
Solution to system (b): x =
y =
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