For Exercises 9-14, assume that the x - and y -axes are rotated through angle θ about the origin to form the x ' - and y ' -axes . (See Example 2) Given θ = 45 ∘ and P − 2 , 5 2 in the x ' y ' -plane, find the coordinates of P in the x y -plane .
For Exercises 9-14, assume that the x - and y -axes are rotated through angle θ about the origin to form the x ' - and y ' -axes . (See Example 2) Given θ = 45 ∘ and P − 2 , 5 2 in the x ' y ' -plane, find the coordinates of P in the x y -plane .
Solution Summary: The author calculates the coordinates of P in the xy -plane when the value of theta =45° and the number of points in it.
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)
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