E) Find all possible solutions, x = < X1, X2, X3, X4, X5 > *=X,<-2,-1, 1,0,0,0+ Xg <-4,1, 2 P,1,0>+X <-3,-1,-1,0,0, 17 t (8,6,6,4,6) F) Express b as a linear combination of vectors from the columns of A in the simplest possible way. G) Express b as a linear combination of vectors from the columns of A with the conditions: X1 + X2 = X3 and x1- X4 = X5.
E) Find all possible solutions, x = < X1, X2, X3, X4, X5 > *=X,<-2,-1, 1,0,0,0+ Xg <-4,1, 2 P,1,0>+X <-3,-1,-1,0,0, 17 t (8,6,6,4,6) F) Express b as a linear combination of vectors from the columns of A in the simplest possible way. G) Express b as a linear combination of vectors from the columns of A with the conditions: X1 + X2 = X3 and x1- X4 = X5.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 32E
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Please answer E, F, G for question #1. （＞人＜；）
![iii) An infinite number of solutions? Why or why not?
M atvix A have two Free Variable,
it have intinite number of solutions.
Here is a vector, b = <8, 6, 6, 4, 6>. The augmented matrix [A | b] has rrer:
%3D
Leading V: X, X2, X
Free Vi XB,X5,Xo
[1 0 2 0 4 3T
0 1 1 0 -1 I
0 0 0 1-2 1
0 0 0 0 0 0
0 0 0 0 0
=X;<-2,-1, 1,0,0,07+ Xg<-4,1,2 D,1,0>#X,<-3,-1,-1,0,0, 1
t(8,6,6,4,67
E) Find all possible solutions, = < x1, X2, X3, X4, X5 >
F) Express b as a linear combination of vectors from the columns of A in the simplest possible way.
G) Express b as a linear combination of vectors from the columns of A with the conditions: X1 + X2 = X3
and x1- X4 = X5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3dcc9212-1f23-45a7-9e3b-eaf4a538ae0a%2F038b48ce-26b3-4038-83b6-a97167b619b7%2F2fr9gga_processed.jpeg&w=3840&q=75)
Transcribed Image Text:iii) An infinite number of solutions? Why or why not?
M atvix A have two Free Variable,
it have intinite number of solutions.
Here is a vector, b = <8, 6, 6, 4, 6>. The augmented matrix [A | b] has rrer:
%3D
Leading V: X, X2, X
Free Vi XB,X5,Xo
[1 0 2 0 4 3T
0 1 1 0 -1 I
0 0 0 1-2 1
0 0 0 0 0 0
0 0 0 0 0
=X;<-2,-1, 1,0,0,07+ Xg<-4,1,2 D,1,0>#X,<-3,-1,-1,0,0, 1
t(8,6,6,4,67
E) Find all possible solutions, = < x1, X2, X3, X4, X5 >
F) Express b as a linear combination of vectors from the columns of A in the simplest possible way.
G) Express b as a linear combination of vectors from the columns of A with the conditions: X1 + X2 = X3
and x1- X4 = X5.
Transcribed Image Text:I5 7 0-
-1 3 1 7
A
4 1 0
-1
4
2 3 -14
3.
-4 2 1 14
1
Here's a matrix, A:
A) It A is the matrix for a linear transform, is it a linear functional, a linear operator, or neither? Why?
A is a 5X5 matix (Suuare)
Linear opeaato
, T:RS_,5 Theretore, it is a
Leading Variable: Xi, Xy Xq
Free Variable: X3, Xe
R= X;<-2, -1, 1,0,074%5(-4,1,0,2,1>
Ker CA)=2,
[1 0 2 0 4
0 1 1 0 -1
rref(A) =0 0 0 1 -2
0 0 0 0 0
Here is the rref(A):
B) Find the rowspace(A), colspace(A) and nullspace(A).
YoWSpacerA):{,0,2,0,4),<0,1, 1,0,-17, <0,0,0, 1,-2>!
colspace A):,2,1,-1,3),51,2,4, 74>,(0,1,13, 15?
nullspace CA):{<-2,4, 1,0,07,<-4,1,0,2,17}
C) What is the dimension of the kernel of A? What is the dimension of the range of A?
dim(ker(A))-2,
dim Cranne CA))3
D) For the matrix equation Ax = b, is it possible that the equation has: O
%3D
i) A unique solution? Why or why not?
A is not a full rank, and it hus 2 Free Variable,
have unique solufion.
RankCA)= RankCA:b), there will besdutlan exist.
sO A does nof
ii) No solutions? Why or why not?
2.
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