Consider the following linear equations :

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 14E: Solve for x,y,z and w in the matrix equation wxyx=-432-1+2ywzx.
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can you please help mw with part e

Consider the following linear equations :
-8x + 4y + 3z
= -4
-8x + (18 – k)y + 2z
= -2
-8x + 4y + (7 – k)z
= k + 2
a)
X1
Suppose the above equation is expressed as Ax = b with x =
X2 . Express the
X3
coeffieints of the equations in one matrix form as (A|b )=
%3D
-8
4
3
-4
18-k
-2
-8
18 – k
2
-2
7-k
k+2
4
-8
7 - k
k + 2
4
Transcribed Image Text:Consider the following linear equations : -8x + 4y + 3z = -4 -8x + (18 – k)y + 2z = -2 -8x + 4y + (7 – k)z = k + 2 a) X1 Suppose the above equation is expressed as Ax = b with x = X2 . Express the X3 coeffieints of the equations in one matrix form as (A|b )= %3D -8 4 3 -4 18-k -2 -8 18 – k 2 -2 7-k k+2 4 -8 7 - k k + 2 4
c)
If the equations have no solution, determine the value of k
4,14
d)
If the equations have infinite number of solutions, determine the value
of k
14
14
e)
Suppose x2 = t with t as any real number. Express the infinite solutions
for the value of k determined in part d) as
X1
X2
t+
X3
Note: only input fractions, e.g. 3/2 or integers.
Transcribed Image Text:c) If the equations have no solution, determine the value of k 4,14 d) If the equations have infinite number of solutions, determine the value of k 14 14 e) Suppose x2 = t with t as any real number. Express the infinite solutions for the value of k determined in part d) as X1 X2 t+ X3 Note: only input fractions, e.g. 3/2 or integers.
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