- 8.4.37: In Exercises 3738, fi nd the products AB and BA to determine whethe...
- 8.4.38: In Exercises 3738, fi nd the products AB and BA to determine whethe...
- 8.4.39: In Exercises 3942, fi nd A-1 . Check that AA-1 = I and A-1A = I A =...
- 8.4.40: In Exercises 3942, fi nd A-1 . Check that AA-1 = I and A-1A = I A =...
- 8.4.41: In Exercises 3942, fi nd A-1 . Check that AA-1 = I and A-1A = I A =...
- 8.4.42: In Exercises 3942, fi nd A-1 . Check that AA-1 = I and A-1A = I A =...
- 8.4.43: In Exercises 4344, a. Write each linear system as a matrix equation...
- 8.4.44: In Exercises 4344, a. Write each linear system as a matrix equation...
- 8.4.45: Use the coding matrix A = J 3 2 4 3 R and its inverse A-1 = J 3 -2 ...
Solutions for Chapter 8.4: Precalculus 5th Edition
Full solutions for Precalculus | 5th Edition
Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined
See Arithmetic sequence.
Composition of functions
(f ? g) (x) = f (g(x))
A measure of the strength of the linear relationship between two variables, pp. 146, 162.
Extracting square roots
A method for solving equations in the form x 2 = k.
Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.
Grapher or graphing utility
Graphing calculator or a computer with graphing software.
Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth
Multiplicative inverse of a matrix
See Inverse of a matrix
Two lines that are at right angles to each other
Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.
Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.
See Division algorithm for polynomials.
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.
Standard form: equation of a circle
(x - h)2 + (y - k2) = r 2
A shift of a graph up or down.
The points x, 0, z in Cartesian space.