Unit 1 Flashcards
Possible number of solutions a linear system can have
3
What are the categories of solutions a system can have
no solution, infinite solutions, 1 solution
meaning of Ax =b
a is a matrix x is a column vector of unknowns and b is column vector of constants
Steps to solve linear equation
1.Write each equation with constants on the right side of the equation and variables on the left size in order
2. build matrix a by collecting all coefficicents while preserving the order
3. build vector x by stacking the unkown variables in order
4 build vector b by stacjing constants in order
Determinant
a real # associated with square matrix that is useful for finding # of sul
how to calculate det with square matrix [[a,b][c,d]]
ad-bc is determininent equation
what does value of det tell
if it is 0 the slopes of the equations are the same with infinite or 0 solutions
if it is not 0 the slopes are different and there is 1 solution
How to multiply vectors
take value of rx * cx and sum them all up where x is size of the array
Identity Matrix
square matrix with 1s on diagonal and 0s elsewhere
When is an equation invertible
when the determinent is not 0
Why do we use vectors
vectors provide us with ways to express an entire set of vectors finitely
vector spaces allow us to communicate linear situations and whether any solutions exist
Requirements for manipulating values
unless it is scalar the vectors must be the same size
Matrix form
the standard table for linear equations (Ax +b)
expanded equation
equation that shows ncolumns of A multiplied by each value in x
linear combinations
equation that shows each value in A being multiplied by its respective x value
