EXAM Flashcards
Linear in R2
Straight Lines
Linear in R3
Shape with straight lines
Linear equations only involve…
+ - scalar multiplication
Is 3x + 5y = 2 linear?
Yes
Is 4 = x^2 + 1 linear?
No
Is 2x + 7y - 0.5z = 0 linear?
Yes
Is -x1 + 5x2 - 18x3 + 3x4 = 6 linear?
Yes
Is 2xy + 4 linear?
No
Systems of linear equations
number of linear equations
Solution of a system
Intersection point of linear equations
Systems of linear equations that have no solution are that way because they are
parallel
A system is consistent if…
there’s at least 1 solution
A system is inconsistent if…
there isn’t at least 1 solution
Linear objects
exactly the possible solution sets to systems of linear equations
2 systems are equivalent if…
they have the same solution sets
Equation operations to change a system of linear equations:
1) swap 2 equations
2) multiply by a non-zero constant
3) add a multiple of 1 equation to another equation
Whenever you apply an equation operation to a system of linear equations…
the new system you get is equivalent to the old one
Row Equivalency
Getting 1 matrix form the other by using a sequence of 3 row operations
If the augmented matrices are row equivalent…
the corresponding systems of linear equations are equivalent
RREF Conditions
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
The method of getting to RREF can be used to…
solve a system of linear equations
A system of linear equations in RREF are inconsistent if…
0 = 1
If a system is consistent then…
it has infinitely many solutions
