MATLAB ASSIGNMENT

2. Find the solution(s) of the following linear systems. Use the MATLAB command rref to immediately find the reduced row echelon form of a matrix. Enter the coefficient matrix A and vector b. When entering the vector b, type b=[b1 b2 b3]'. The ' indicates transpose and changes b from a row vector to a column vector. Type rref([A b]). This is asking for the reduced row echelon form of the augmented matrix [A b]. For each system write by hand all solutions (or state that there is no solution) on your printout near the problem.

(a)

2x1	+	x2	+	3x3	+	2x4	=	-4
-x1			-	x3	+	x4	=	2
3x1	-	2x2	+	x3	+	4x4	=	-21
4x1	+	7x2	+	5x3	+	4x4	=	12

(b)

2x1

+

6x2

-

3x3

-

x4

+

18x5

+

2x6

=

-103

x2

+

3x3

+

4x4

+

12x5

+

9x6

=

-61

-2x1

+

3x2

-

5x5

+

6x6

=

63

-x1

+

7x2

+

8x3

+

12x4

+

39x5

+

x6

=

-208

7x1

+

4x2

-

3x3

+

5x4

+

66x5

=

-469

(c)

2x1	+	6x2	-	3x3	=	-1
		x2	+	x3	=	4
-2x1	+	3x2			=	0
-x1	+	7x2	+	8x3	=	12
7x1	+	4x2	-	3x3	=	5

(d)

x1	-	x2	+	x3	-	x4	=	0
x1	+	2x2	-	3x3	+	4x4	=	0
3x1	-	x2	+	2x3	+	4x4	=	0
	-	x2	-	x3	+	2x4	=	0