For Exercises 9-32, solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. (See Examples 2-5) x − 2 y + z = − 9 3 x + 4 y + 5 z = 9 − 2 x + 3 y − z = 12
For Exercises 9-32, solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. (See Examples 2-5) x − 2 y + z = − 9 3 x + 4 y + 5 z = 9 − 2 x + 3 y − z = 12
Solution Summary: The author explains how to calculate the solution of the given system of equations.
For Exercises 9-32, solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. (See Examples 2-5)
x
−
2
y
+
z
=
−
9
3
x
+
4
y
+
5
z
=
9
−
2
x
+
3
y
−
z
=
12
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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