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Algebra II Spring 2022 > SYMKC Week 6 > Flashcards

SYMKC Week 6 Flashcards

1
Q

In order to multiply two matrices, (m X n) (n X p)

A

the inner dimensions must be the same

the “n”

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2
Q

We can add and subtract two matrices if ______

A

the dimensions are the same

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3
Q

Name the ways you could solve a system

A
  1. Substitution
  2. Elimination
  3. Graphing
  4. Technology
  5. Matrices
  6. Cramer’s Rule
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4
Q

There is no defined process for _______ a matrix by a matrix

A

dividing

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5
Q

another name for rectangular arrangement

A

array

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6
Q

a method for solving systems of linear equations that involves adding the multiple of one equation to the multiple of another equation with the goal of eliminating a variable.

A

elimination

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7
Q

the individual values of a matrix

A

elements

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8
Q

a rectangular arrangement of numbers

A

matrix

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9
Q

Uses of a determinant

A

1) solving systems of linear equations

2) finding inverses for matrices

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10
Q

represents a system of equations written in standard form. It includes the variables’ coefficients in the first three columns and the constant term in the final column

A

augmented matrix

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11
Q

the solution to a three variable system of equations may be represented by _______.

A

an ordered triple (x, y, z)

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12
Q

the number of elements of a matrix is the ____________

A

product of the number of row and the number of columns

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13
Q

Symbolism for the inverse of a matrix A

A
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14
Q
A

zero matrix

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15
Q

Two matrices are equal if and only if

A

the order (or dimensions) are the same and the corresponding elements are the same

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16
Q

Instead of a process for dividing matrices, we

A

multiply both sides by an inverse.

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17
Q

How many solutions will result with the system?

A

None - all three planes do not intersect

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18
Q

matrix addition is _______ and ________.

A

commutative and associative

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19
Q

The solution a two variable system of equations may be represented by _______.

A

an ordered pair (x, y)

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20
Q

A 3 X 3 system of equations with __________ will produce a matrix with the final row in the form of [0 0 0 | 0. This is interpreted as 0x +0y +0z = 0, or 0 = 0

A

infinitely many solutions

21
Q

Formula for Cramer’s Rule for the system below

A
22
Q

A determinant can only be found with ________ matrices

A

square

23
Q

To find the sum or difference between two matrices, we add or subtract _____________.

A

corresponding elements

24
Q

Formula for the Inverse of any matrix

A
25
Q

another name for dimensions of a matrix

A

order

26
Q

this occurs when one of the variables will eliminate, resulting in a true statement such as 0=0. This occurs when the planes intersect in a line or when the planes are stacked exactly on top of each other

A

infinitely many solutions

27
Q

Formula for the determinant of the following matrix 2 X 2

A
28
Q

symbolism that represents a determinant of matrix A

A

A |

29
Q

A matrix is labeled with _____.

A

Capital letter

30
Q

matrix subtraction is _____ commutative and is ____ associative

A

NOT

31
Q

this occurs when the three planes (represented by the three equations) intersect at one location

A

exactly one point

32
Q

When solving with augmented matrices a 3 X 3 system of equations with ________ will produce a matrix with the final row in the form [0 0 0 | 1}. This represents 0x + 0y + 0z =1; 0=1 which is a false statement

A

no solution

33
Q

The inverse of a matrix is similar to the ______ of a number

A

reciprocal

34
Q

another name for a real number outside of a matrix with the intent to multiply through the matrix

A

scalar

35
Q

with two matrices of size m X n) and (n X p), what would the resulting size be if you multiplied these together?

A

m X p

36
Q

a method for solving systems of linear equations that involves solving one equation for a specific variable and substituting the new expression into other equation(s) with the goal of eliminating a variable

A

substitution

37
Q

In scalar multiplication, multiply each ______ by the scalar (real number)

A

entry

38
Q

a useful number that can be calculated from the elements of a matrix

A

determinant

39
Q

the sum of products of corresponding values

(x,y) (a, b) = xa + yb

A

Dot product

40
Q

the order in which we add numbers does not matter

A

commutative

41
Q

represents a system of equations written in standard form. It includes a matrix for the coefficients of the variables, a matrix for the variable, and a matrix for the constants

A

Matrix Equation

42
Q

How many solutions are in the system?

A

Infinitely many, a line is the intersection between the three planes

43
Q

uses the coefficient matrix and determinants to solve a system of linear equations

A

Cramer’s Rule

44
Q

the number of rows is equal to the number of columns in a matrix

A

square matrix

45
Q

How many solutions will result with the system?

A

one (x, y, z)

46
Q

The number of rows and the number of columns in a matrix

A

dimensions

47
Q

this occurs when one of the variables will eliminate, resulting in a false statement, such as 0 = 1. This occurs when there is no location where all three planes intersect.

A

no solution

48
Q

A matrix added to the zero matrix is the ______ matrix

A

original

49
Q

If A and B are both matrices, how do you solve for X

A

Algebra II Spring 2022 (8 decks)

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