In Exercises 5 and 6, write a system of equations that is equivalent to the given vector equation 6. x 1 [ − 2 3 ] + x 2 [ 8 5 ] + x 3 [ 1 − 6 ] = [ 0 0 ]
In Exercises 5 and 6, write a system of equations that is equivalent to the given vector equation 6. x 1 [ − 2 3 ] + x 2 [ 8 5 ] + x 3 [ 1 − 6 ] = [ 0 0 ]
Solution Summary: The author explains the system of equations for the vector equation.
In Exercises 5 and 6, write a system of equations that is equivalent to the given vector equation
6.
x
1
[
−
2
3
]
+
x
2
[
8
5
]
+
x
3
[
1
−
6
]
=
[
0
0
]
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
A box containing five, ten, and twenty-dollar bills, has 130 bills in it with a total
value of $2560. Find how many bills of each type are in the box by setting up and
solving a system of linear equations.
Suppose the solution set of a system of linear equations can be described as
x₁ = 2-5x4
x₂ = -4x4
x3 = 5 +9x4
with 4 free.
a. Write the solution to this system in parametric vector form.
x = DNE x+x4
6. Consider the following system of four linear equations in five variables.
2x1 + 4x2 – 2x3 + 2x4 + 4x3 = 2
xị+ 2x2 – x3+ 2x4 = 4
3x1 + 6x2 – 2x3 + x4 + 9x5 = 1
5x1 + 10r2 – 4x3 + 5x4 + 9x5 = 9
|
(a) Write a vector equation that is equivalent to this linear system, and a matrix equation that is equivalent
to this linear system.
(b) Determine the solution set of this linear system, and express it in parametric vector form.
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