Chapter 11 (Alg 2)

Question 1

Matrix

Answer 1

A rectangular arrangement of numbers in horizontal rows and vertical columns

Question 2

Element

Answer 2

A number in the matrix

Question 3

Dimensions Of A Matrix

Answer 3

“m x n”

Rows by columns

Question 4

Equal (Matrices)

Answer 4

dimensions are the same and elements are in corresponding positions

Question 5

Adding and Subtrating Matrices

Answer 5

only if they have the same dimensions

Question 6

Scalar

Answer 6

In operations with matrices, a real number is called a scalar

Question 7

Scalar Multiplication

Answer 7

Multiplying a Matrix by a scalar, you multiply each element by the scalar

Question 8

Properties of Matrix Addition and Subraction

Answer 8

Let A, B and C be matrices with the same dimension, and let k be a scalar:
APOA (A + B) + C = A + (B + C)
CPOA A + B = B + A
DPOA k(A + B) = kA + kB
DPOS k(A - B) = kA - kB

Question 9

Multiplying Matrices

Answer 9

If the # of columns in A is = the # rows in B; you can multiply them, it’s defined.
If the dimensions of A are m x n and dimensions of B are n x p, then the dimensions of the product AB are m x p

Question 10

Maxtrix Multiplication

Answer 10

multiply the elements of each row of the first matrix by the elements of each column of the second matrix, and then add the products

Question 11

Properties of Matrix Multiplication

Answer 11

Let A, B and C be matrices
APOM A(BC)
LDP A(B + C) = AB + AC
RDP (A + B)C = AC + BC

Question 12

Identity Matrix

Answer 12

A matrix that has 1’s on the main diagonal and 0’s elsewhere
{}
If A is any n x n matrix and I is the n x n identity matrix, then IA = AI = A

Question 13

Inverse matrices

Answer 13

if the product of two matrices (in both orders) is the n x n identity matrix
{}
You can use the calc to find the inverse of a matrix

Question 14

System of linear equations in standard form

Answer 14

AX = B
A is the coefficient matrix
X is the matrix of variables
B is the matrix of constants

Question 15

Solution of the linear equations

Answer 15

X = A^-1 B

Multiply the inverse of matrix A by matrix B

Question 16

Determinant

Answer 16

Associated with each sqaure (n x n) matrix is a real number called its determinant
Denoted by det A or |A|

Question 17

The determinant of a 2 x 2 matrix

Answer 17

the difference of the products of the elements on the diagonals

Question 18

Cramer’s Rule

Answer 18

using the determinant to solve a system of linear equations

Question 19

Cramer Rule for a 2 x 2 system

Answer 19

Let A be the coefficient matrix of the linear system
{}
ax + by = e ; cx + dy = f {a b
c d}
- - - - - - - - - - - - -
If det A DNE 0, then the system has exactly one solution. The solution is:
|e b| |a e|
x = |f d| y = |c f|
——- ——-
|A| |A|

Question 20

Sequence

Answer 20

A fucntion whose domain is a set of consectuive integers

Question 21

Terms

Answer 21

Values in the range of the function

Question 22

Finite, Infinite sequences

Answer 22

1,2,3,4 ; 1,2,3,4 . . .

Question 23

Series

Answer 23

When the terms of a sequence are added together

Question 24

Formulas for special series

Answer 24

n terms / 1 + 1 + 1 + 1 + 1 + 1 . . . = n
1 + 2 + 3 + 4 + 5 . . . = n(n + 1) over 2
1^2 + 2^2 + 3^2 + 4^2 . . . = n(n + 1)(2n + 1) over 6

Question 25

Arithmetic Sequence

Answer 25

the difference between the terms is the same

Question 26

Common difference

Answer 26

the constant difference is called the common difference and is denoted by d

Question 27

Rule for an Arithmetic Sequence

Answer 27

The nth term of an arithmetic sequence with first term a sub 1 and common difference d can be found using the following rule.
a sub n = a sub 1 + (n - 1)d

Question 28

Arithmetic series

Answer 28

adding the terms of an arithmetic sequence

Question 29

The sum of a finite Arithmetic Series

Answer 29

The sum of the first n terms of an arithmetic series is given by the following formula
S sub n = n(a sub 1 + a sub n all over 2)

Question 30

Geometric Sequence

Answer 30

the ratio of any term to the previous term is constant

Question 31

Common Ratio

Answer 31

the constant ratio and is denoted by r

Question 32

Rule for a Geometric Sequence

Answer 32

The nth term ofa geometric sequence with first term a sub 1 and common ratio r can be found using the following rule.
a sub n = a sub 1 r^(n-1)

Question 33

Geometric Series

Answer 33

the expression formed by adding the terms of a geometric sequence

Question 34

The sum of a finite Geometric Series

Answer 34

The sum of the first n terms of a geometric series with common ratio r when r DNE 1, is given by the following formula:
S sub n = a sub 1 (1 - r^n over 1 -r)

Question 35

The Sum of an infinite Geometric Series

Answer 35

The sum of an infinite geometric series with first term a sub 1 and common ratio r is given by:
S = a sub 1 / 1 - r
|r| = 1, the series has no sum

Question 36

Write a repeating Decimal as a Fraction

Answer 36

Example: 0.17171717…
0.17171717… = 0.17 + 0.0017 + 0.000017 . . .
= 17(0.01) + 17(0.01)^2 + 17(0.01)^3 . . .
= 17(0.01) over 1 - 0.01
= 17/99