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MAT 1302 > EXAM > Flashcards

EXAM Flashcards

1
Q

Linear in R2

A

Straight Lines

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2
Q

Linear in R3

A

Shape with straight lines

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3
Q

Linear equations only involve…

A

+ - scalar multiplication

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4
Q

Is 3x + 5y = 2 linear?

A

Yes

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5
Q

Is 4 = x^2 + 1 linear?

A

No

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6
Q

Is 2x + 7y - 0.5z = 0 linear?

A

Yes

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7
Q

Is -x1 + 5x2 - 18x3 + 3x4 = 6 linear?

A

Yes

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8
Q

Is 2xy + 4 linear?

A

No

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9
Q

Systems of linear equations

A

number of linear equations

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10
Q

Solution of a system

A

Intersection point of linear equations

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11
Q

Systems of linear equations that have no solution are that way because they are

A

parallel

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12
Q

A system is consistent if…

A

there’s at least 1 solution

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13
Q

A system is inconsistent if…

A

there isn’t at least 1 solution

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14
Q

Linear objects

A

exactly the possible solution sets to systems of linear equations

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15
Q

2 systems are equivalent if…

A

they have the same solution sets

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16
Q

Equation operations to change a system of linear equations:

A

1) swap 2 equations
2) multiply by a non-zero constant
3) add a multiple of 1 equation to another equation

17
Q

Whenever you apply an equation operation to a system of linear equations…

A

the new system you get is equivalent to the old one

18
Q

Row Equivalency

A

Getting 1 matrix form the other by using a sequence of 3 row operations

19
Q

If the augmented matrices are row equivalent…

A

the corresponding systems of linear equations are equivalent

20
Q

RREF Conditions

A

1) Every row of zeros is below all not-all-zero rows
2) The leftmost nonzero entry in any row is 1 (leading 1)
3) Every leading 1 is the only nonzero entry in its column
4) If a leading 1 is to the left of another leading 1, it is also above that leading 1

21
Q

The method of getting to RREF can be used to…

A

solve a system of linear equations

22
Q

A system of linear equations in RREF are inconsistent if…

A

0 = 1

23
Q

If a system is consistent then…

A

it has infinitely many solutions

MAT 1302 (2 decks)

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