matrix Flashcards
what is linear algebra
a branch of mathematics that deals with systems of linear equations
which is the independent variable
x
which is the dependent variable
y
how to solve simultaneous equations
sum up equations removing a variable and find left over variable
substitute value for one into the other
what is a 2X2 determinant based on
denominator of general equation for solving simultaneous equations
equation for 2X2 determinant
a1b2 - b1a2
what does a a1b2 - b1a2 determinant look like
a1 b1
a2 b2
how to find D from a 2X2
cross multiply a1 minus cross multiple b1
what is the solution to any set of two linear equations
x = Dx/D y = Dy/D
what is Dx
c1 b1
c2 b2
what Dy
a1 c1
a2 c2
what is a matrix
an array of numbers
what is a m x n
m rows and n columns
address of element
row i column j
like aij
what variable is a on
x
what makes a matrix equal
literally everything
when can you add matrix
when they have the same order
how to add matrix
just add equivalent numbers
how to multiply by a constant
just multiply every value by the constant
how to multiply matrix
row by column
far left to top
then add them and it is one number if one row by one column matrix
when can you multiply matrix
when the number of columns of the first one equals the number of columns of the second
how to find the size of the matrix after multiplication
columns of A by rows of B
how to multiply matrix with more than one row/column
multiply first row and column and add to get a number
then first row and second column then second row and first column then second row and second column
what is a commutative law
you can add/multiply in any order
