- 11-7.R.0: Update your journal with what you have learned in this chapter. Inc...
- 11-7.R.1: Figure 11-7a shows a line segment 1 unit long. In the first iterati...
- 11-7.R.2: a. Evaluate: b. Evaluate: c. Evaluate: det d. Solve this system by ...
- 11-7.R.3: a. Describe the transformations produced by matrix [T]. b. Plot the...
- 11-7.R.4: a. Describe the transformations produced by matrix [A]. b. Plot the...
- 11-7.R.5: Figure 11-7b shows the rectangular pre-image It also shows the imag...
- 11-7.R.6: a. State the definition of the Hausdorff dimension. b. Show that th...
- 11-7.C.1: Research 2: Explore literature about fractals. From the information...
- 11-7.T.1: Multiply:
- 11-7.T.2: Explain why the matrices in are commensurate for multiplication. T
- 11-7.T.3: In what way is matrix multiplication similar to the multiplication ...
- 11-7.T.4: Find det . Use the result to find . Show that the product of the ma...
- 11-7.T.5: What transformation is represented by this matrix? T
- 11-7.T.6: A line segment is transformed by iterative matrix multiplication. T...
- 11-7.T.7: Write three 3 3 transformation matrices to do the following: [A] sh...
- 11-7.T.8: Multiply each of [A], [B], and [C] by the pre-image matrix. Write t...
- 11-7.T.9: The three images in are the results of the first iteration. If the ...
- 11-7.T.10: If the iterations are done infinitely many times, the resulting tre...
- 11-7.T.11: Figure 11-7e shows the strange attractor from plotted with 1000 poi...
- 11-7.T.12: The first iteration has three images, each 5 units long. The second...
- 11-7.T.13: If the iterations were performed infinitely many times, what would ...
- 11-7.T.14: Each iteration divides each previous segment into three self-simila...
- 11-7.T.15: Complete the statement: Each time is multiplied by 2, N is multipli...
- 11-7.T.16: Write Hausdorffs definition of dimension. T1
- 11-7.T.17: Calculate the dimension of the tree that would result if the iterat...
- 11-7.T.18: Strange attractors such as the one in Figure 11-7e result from iter...
- 11-7.T.19: What did you learn as a result of taking this test that you did not...
Solutions for Chapter 11-7: Matrix Transformations and Fractal Figures
Full solutions for Precalculus with Trigonometry: Concepts and Applications | 1st Edition
Composition of functions
(f ? g) (x) = f (g(x))
Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.
Grapher or graphing utility
Graphing calculator or a computer with graphing software.
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.
Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.
Inverse secant function
The function y = sec-1 x
The notation dy/dx for the derivative of ƒ.
Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0
Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.
Two vectors u and v with u x v = 0.
Two lines that are both vertical or have equal slopes.
An arrangement of elements of a set, in which order is important.
Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)
Principle of mathematical induction
A principle related to mathematical induction.
Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc - ad c2 + d2 i
The principle of experimental design that makes it possible to use the laws of probability when making inferences.
a - b = a + (-b)
Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.