4. Find the value of k for which the system of equations 31 -2-2r3 =12x1 + 3rg - 5r3is consistent= k:5. Find the value of k for which the system of equations 3-1-1321+ 5r, + 5r, = k= 4 is inconsistent2n - 3r2 +I3 = 06. Find the value of k for which the system of equations n+ 2r2 - 3rs = 0 has non trivial4r - 12+ krs = 0solutions.7. Use the Gaussian elimination method to find the solution set of the following systems and thatof their associated homogeneous forms.a + 2r, - = 1= 23r, - 5r, = 3a) 211 + 4r2I1 - 12 + I3 = 1b) 3z15x1 - 2r2 +3r = 5+ I3 =38. Suppose that the augmented matrix corresponding to some linear system Ax = b reduces tothe following:1 20 0 7 0 0| 180 0 1 00 04.0 0 0 1 -3 0 00 0 0 0 0 0 1 p0 0 0 0 0 o 0 k(a) Using your own unknown variables for the given reduced system, identify the basic andfree variables.(b) What conditions (if any) are there on r, p, k so that(i) there are no solutions to Ax = b(ii) there is exactly one solution to Ax = b(ii) there are infinitely many solutions to Ax = b9. Consider the matrix-13A =2-26.(a) If A is the augmented matrix of a system of linear equations, determine the mumber ofequations and the number of variables.

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Answered: 5. Find the value of k for which the…

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5. Find the value of k for which the system of equations 31 - 1 - 1 = 4 is inconsistent I1+5r, + 5r, = k

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 2BEXP

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Question

4. Find the value of k for which the system of equations 31 -2-2r3 =1
2x1 + 3rg - 5r3
is consistent
= k:
5. Find the value of k for which the system of equations 3-1-13
21+ 5r, + 5r, = k
= 4 is inconsistent
2n - 3r2 +I3 = 0
6. Find the value of k for which the system of equations n+ 2r2 - 3rs = 0 has non trivial
4r - 12+ krs = 0
solutions.
7. Use the Gaussian elimination method to find the solution set of the following systems and that
of their associated homogeneous forms.
a + 2r, - = 1
= 2
3r, - 5r, = 3
a) 211 + 4r2
I1 - 12 + I3 = 1
b) 3z1
5x1 - 2r2 +3r = 5
+ I3 =3
8. Suppose that the augmented matrix corresponding to some linear system Ax = b reduces to
the following:
1 20 0 7 0 0| 18
0 0 1 0
0 0
4.
0 0 0 1 -3 0 0
0 0 0 0 0 0 1 p
0 0 0 0 0 o 0 k
(a) Using your own unknown variables for the given reduced system, identify the basic and
free variables.
(b) What conditions (if any) are there on r, p, k so that
(i) there are no solutions to Ax = b
(ii) there is exactly one solution to Ax = b
(ii) there are infinitely many solutions to Ax = b
9. Consider the matrix
-1
3
A =
2
-2
6.
(a) If A is the augmented matrix of a system of linear equations, determine the mumber of
equations and the number of variables.

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