For Exercises 23-28, a. Determine an acute angle of rotation to eliminate the x y -term . (See Example 4) b. Use a rotation of axes to eliminate the x y -term to write the equation in the form A ' x ' 2 + C ' y ' 2 + D ' x ' + E ' y ' + F ' = 0 . c. Identify the type of curve represented by the equation. d. Write the equation in standard form and sketch the graph. 3 x 2 − 10 3 x y + 13 y 2 + 18 = 0
For Exercises 23-28, a. Determine an acute angle of rotation to eliminate the x y -term . (See Example 4) b. Use a rotation of axes to eliminate the x y -term to write the equation in the form A ' x ' 2 + C ' y ' 2 + D ' x ' + E ' y ' + F ' = 0 . c. Identify the type of curve represented by the equation. d. Write the equation in standard form and sketch the graph. 3 x 2 − 10 3 x y + 13 y 2 + 18 = 0
Solution Summary: The author explains how to eliminate the xy term by rotating the equation at an angle of 30°.
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.
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