For Exercises 47, 56, sketch a graph that possesses the characteristics listed Answers may vary f ' ( − 1 ) = 0 , f " ( − 1 ) > 0 , f ( − 1 ) = − 2 , f ' ( 1 ) = 0 , f " ( 1 ) > 0 , f ( 1 ) = − 2 , f ' ( 0 ) = 0 f " ( 0 ) < 0 and f ( 0 ) = 0
For Exercises 47, 56, sketch a graph that possesses the characteristics listed Answers may vary f ' ( − 1 ) = 0 , f " ( − 1 ) > 0 , f ( − 1 ) = − 2 , f ' ( 1 ) = 0 , f " ( 1 ) > 0 , f ( 1 ) = − 2 , f ' ( 0 ) = 0 f " ( 0 ) < 0 and f ( 0 ) = 0
Solution Summary: The author explains that there are many possibilities to draw a graph of given characteristics. Label the graph paper by the points (0.1),
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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