Question

Solve the system

-2x1+4x2+5x3=-22

-4x1+4x2-3x3=-28

4x1-4x2+3x3=30

a)the initial matrix is:

b)First, perform the Row Operation 1/-2R1->R1. The resulting matrix is:

c)Next perform operations

+4R1+R2->R2

-4R1+R3->R3

The resulting matrix is:

d) Finish simplyfying the augmented mantrix down to reduced row echelon form. The reduced matrix is:

e) How many solutions does the system have?

f) What are the solutions to the system?

x1 =

x2 =

x3 =

Answer #1

(a) The augmented matrix for the given system of equation is as follows,

(b) First, perform the Row Operation 1/-2R1->R1. The resulting matrix is:

(c) Next perform operations

+4R1+R2->R2

-4R1+R3->R3

The resulting matrix is:

(D) Divide R2 by -4 so we get,

Multiply R2 by 2 and add with R1

Now multiply R2 by 4 and subtract it from R3 to get R3

(e) Since for last row we get 0 = 2 as result, which is not possible.

So there is no solution to this system of equation.

(f) Since the system has no solution we cannot find the value of x1, x2, x3

.

2X1-X2+X3+7X4=0
-1X1-2X2-3X3-11X4=0
-1X1+4X2+3X3+7X4=0
a. Find the reduced row - echelon form of the coefficient
matrix
b. State the solutions for variables X1,X2,X3,X4 (including
parameters s and t)
c. Find two solution vectors u and v such that the solution
space is \
a set of all linear combinations of the form su + tv.

Use the Gauss-Jordan reduction to solve the following linear
system:
x1-x2+5x3=-4
5x1-4x2+3x3=-9
2x1 -34x3=14

Solve the following system using augmented matrux methods
-3x+6y = 0
-4x +6y = 0
a) The initial matrix is:
b) First, perform the Row Operation 1/-3R1->R1. The resulting
matrix is:
c) Next, perform the operation +3R1+R2->R2. The resulting
matrix is:
d) Finish simplifying the augmented matrix. The reduced matrix
is:
e) How many solutions does the system have?
f) What are the solutions to the system?
x =
y =

Given that the matrix
[[-3,-7,-2,0],[3,0,-6,0],[1,7,-2,0]]
is the augmented matrix for a linear system, use technology to
perform the row operations needed to transform the matrix to
reduced echelon form. Then determine if the system is consistent
and if it is, find all solutions to the system.
Reduced echelon form:
Is the system consistent? select yes no
Solution: (x1,x2,x3)=

Solve the following systems by forming the augmented matrix and
reducing to reduced row echelon form. In each case decide whether
the system has a unique solution, infinitely many solutions or no
solution. Show pivots in squares. Describe the solution set.
-3x1+x2-x3=10
x2+4X3=12
-3x1+2x2+3x3=11

Solve the following system of linear equations: 3x2−9x3 = −3
x1−2x2+x3 = 2 x2−3x3 = 0 If the system has no solution, demonstrate
this by giving a row-echelon form of the augmented matrix for the
system. If the system has infinitely many solutions, your answer
may use expressions involving the parameters r, s, and t. You can
resize a matrix (when appropriate) by clicking and dragging the
bottom-right corner of the matrix.

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