chapter 7

Question 1

how to determine number of solutions from a system

Answer 1

graph and count

Question 2

finding value of constant so system is dependent

Answer 2

factor of other equation that will m ake them equal

Question 3

finding value of constant so system is independent

Answer 3

if lines have sane slope, not possible, either intersect 0 or inifintely many times

Question 4

finding value of constant so system is inconsistent

Answer 4

any solution not equal to the vale that makes the same

Question 5

matrix

Answer 5

a rectangular array of rows and columns of real numb ers

Question 6

matrix of order mxn

Answer 6

has m rows and n columns

Question 7

element of matrix

Answer 7

uses double subscript notation so arc indicatiesrow and column of matrix A

Question 8

two matrices equal

Answer 8

same size and soorespponding elements are equal

Question 9

augmented matrix

Answer 9

coefficients of each variable are set up in columns, followed by a vertical bar, and then a column of constants

Question 10

steps to finding a general solution

Answer 10

1. since the bottom row is all zeros, z=z
2. take the other rows of the matrix and turn them back into equations
3. solve the middle equation for y in terms of z
4. solve the top equation for x in terms of z
5. write the ordered triple in terms of z. then sub in value besides 0 to find a specific solution
6. check

Question 11

purpose of pfd

Answer 11

rewrite a tational function with higher degrees as the sum of rational expressions with lower degrees

Question 12

four cases considering

Answer 12

1. denominator is a product of distinct linear factors
2. denominator is a product of linear factors, some of which are repeated
3. denominator has prime quadratic factors, none of which is repeated
4. the denominator has a repeated prime quadratic factor

Question 13

denominator is a product ofdifferent linear factors

Answer 13

numerators are A, B, etc. with each factor in denominator

Question 14

linear factors with a repeated factor

Answer 14

numerators are A, B, etc. with factor that repeates the squared cubed etc

Question 15

prime quadratic factors, no repeats

Answer 15

A above normal facors then bx+c above quadratics

Question 16

when setting up pfd

Answer 16

numerator has to have a degree of one less than the denominators

Question 17

repeated quadratic factor, same as above except

Answer 17

use squared and cubed for repeated factors etc

Question 18

dont multiply by lcd

Answer 18

multiply by dneominator