- 12-184.108.40.206: Evaluate the following expressions given that: R = 3 7 2 1 and S = ...
- 12-220.127.116.11: Evaluate the following expressions given that: A = 2 57 4 6 3 16 5 ...
- 12-18.104.22.168: Evaluate the following expressions given that: U = 3 2 51 4 6 73 1 ...
- 12-22.214.171.124: Let R and S be the matrices from 1, and let p = (3, 1) and q = (1, ...
- 12-126.96.36.199: Let A and B be the matrices defined in 2, and let u = (3, 2, 5) and...
- 12-188.8.131.52: Let U and V be the matrices defined in 3, and let s = (2, 0, 1, 7) ...
- 12-184.108.40.206: Let A and B be the matrices given by A = 3 7 2 1 and B = 1 5 0 0 1 ...
- 12-220.127.116.11: Let A = 1 2 2 1 and u = (5, 5). (a) Find w such that w = Au . (b) F...
- 12-18.104.22.168: A new virus emerges in a population. Each day, 10% of the susceptib...
- 12-22.214.171.124: A new virus emerges in a population. Each day, 10% of the susceptib...
- 12-126.96.36.199: Let p 2005 = (A2005, B2005) = (200, 400) describe the populations (...
- 12-188.8.131.52: Let I2 = 1 0 0 1 and I3 = 100 010 001 . (a) Evaluate I2u for (i) u ...
- 12-184.108.40.206: In an algebraic equation such as y = kx, k = 0, we can multiply thr...
- 12-220.127.116.11: In 13, we introduced the notion of the inverse of a matrix A, writt...
- 12-18.104.22.168: Multiplying a vector by a matrix is a much more complicated process...
- 12-22.214.171.124: This is where matrix multiplication comes in: if we think of c1 and...
- 12-126.96.36.199: Let v = (2, 5), c1 = (3, 2), and c2 = (5, 4). In this problem we wi...
- 12-188.8.131.52: Following the procedure outlined in 17, write v = (5, 8) as a combi...
Solutions for Chapter 12-5: MATRICES
Full solutions for Functions Modeling Change: A Preparation for Calculus | 4th Edition
The gathering and processing of numerical information
Difference of two vectors
<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>
The number found when the corresponding components of two vectors are multiplied and then summed
The right side of u(v + w) = uv + uw.
An equation written with exponents instead of logarithms.
Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.
Events A and B such that P(A and B) = P(A)P(B)
A procedure for fitting a logistic curve to a set of data
A function viewed as a mapping of the elements of the domain onto the elements of the range
Mode of a data set
The category or number that occurs most frequently in the set.
A function in which ƒ(x)is a polynomial in x, p. 158.
A 90° angle.
A process for gathering data from a subset of a population, usually through direct questioning.
Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true
Solve a system
To find all solutions of a system.
Standard form of a complex number
a + bi, where a and b are real numbers
A procedure used to divide a polynomial by a linear factor, x - a
A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.
The numbers 0, 1, 2, 3, ... .
The y-value of the top of the viewing window.