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Exercises Names Solve the following systems of equations using augmented matrices and the rref command in MATLAB. Determine the augmented matrix, the equivalent form as transformed by rref, write down the new transformed system of equations from the rref result, and the solution, if any. Also write out the vector form of the equations and the solution in parametric form. Identify the particular, $p$, and homogeneous, $v_h$, parts of the vector form. Indicate the number of pivots and circle the pivot columns of the augmented matrix. 1. Determine: augmented matrix, rref equivalent form, and the solution, if any. Augmented matrix: $\begin{bmatrix} 1 & -1 & 3 \\ 2 & 1 & 3 \end{bmatrix}$ x - y = 3 2x + y = 3 rref result: new equation from rref result: Number of pivots Solution: x = y = p = $v_h = $ Vector form of solution: Parametric form of solution: 2. Determine: augmented matrix, rref equivalent form, and the solution, if any. 10x + 15y = 20 2x + 3y = 4 Augmented matrix: rref result: new equation from rref result: Number of pivots Solution: x = y = p = $v_h = $ Free variables Solution type: Free variables Solution type: Vector form of solution: Parametric form of solution: 1

          Exercises
Names
Solve the following systems of equations using augmented matrices and the rref command in
MATLAB. Determine the augmented matrix, the equivalent form as transformed by rref, write
down the new transformed system of equations from the rref result, and the solution, if any. Also
write out the vector form of the equations and the solution in parametric form. Identify the
particular, $p$, and homogeneous, $v_h$, parts of the vector form. Indicate the number of pivots and
circle the pivot columns of the augmented matrix.
1. Determine: augmented matrix, rref equivalent form, and the solution, if any.
Augmented matrix:
$\begin{bmatrix} 1 & -1 & 3 \\ 2 & 1 & 3 \end{bmatrix}$
x - y = 3
2x + y = 3
rref result:
new equation from rref result:
Number of pivots
Solution: x = 
y =
p =
$v_h = $
Vector form of solution:
Parametric form of solution:
2. Determine: augmented matrix, rref equivalent form, and the solution, if any.
10x + 15y = 20
2x + 3y = 4
Augmented matrix:
rref result:
new equation from rref result:
Number of pivots
Solution: x = 
y =
p =
$v_h = $
Free variables
Solution type:
Free variables
Solution type:
Vector form of solution:
Parametric form of solution:
1

Exercises
Names
Solve the following systems of equations using augmented matrices and the rref command in
MATLAB. Determine the augmented matrix, the equivalent form as transformed by rref, write
down the new transformed system of equations from the rref result, and the solution, if any. Also
write out the vector form of the equations and the solution in parametric form. Identify the
particular, p, and homogeneous, vh, parts of the vector form. Indicate the number of pivots and
circle the pivot columns of the augmented matrix.
1. Determine: augmented matrix, rref equivalent form, and the solution, if any.
Augmented matrix:
< b m a t r i x >
x - y = 3
2x + y = 3
rref result:
new equation from rref result:
Number of pivots
Solution: x =
y =
p =
vh =
Vector form of solution:
Parametric form of solution:
2. Determine: augmented matrix, rref equivalent form, and the solution, if any.
10x + 15y = 20
2x + 3y = 4
Augmented matrix:
rref result:
new equation from rref result:
Number of pivots
Solution: x =
y =
p =
vh =
Free variables
Solution type:
Free variables
Solution type:
Vector form of solution:
Parametric form of solution:
1

Added by Brenda R.

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