Final Exam Flashcards
Vectors Matrices (2x2, 3x2, 3x3) Determine Size of Matrix Determine if Multiplication is possible Inverse Determinant (2x2) Determinant (3x3) Determine if Inverse is possible Craimers Rule 2 Exp Crammers Rule 3 Exp
How do you calculate a vector answer
Horizontal Times Vertical (add each digits products together)
What is the formula for determining the size of the new matrix
Rows in #1 = Columns in #2
How do you determine if multiplying a matrix is possible?
Columns in #1 = Rows in #2
How do you multiply a 2x2 or 3x2 or 3x3 Matrix
Take the horizontal row in #1 and multiply by vertical column in #2 …. until all numbers are populated
What is the formula for the Inverse
1
___ X adj (A)
det(A)
What is the formula for the determinant of a 2x2
ad-bc
What is the formula for a determinant of a 3x3
Build 3 row, 5 column table by repeating the first 2 columns
How do you know if a determinant isn’t possible?
ad-bc = 0
How do you build A using Cramers rule in a 2 exponent equation?
ex: 4x + 3y = -23
3x - 5y = 19
[ 4 3]
[ 3 5]
A = x (eq1) , y (eq 1)
x (eq2) , y (eq1)
How do you build A-1 using Cramers rule in a 2 exponent equation?
ex: 4x + 3y = -23
3x - 5y = 19
[-23 3]
[ 19 -5]
A-1 = Prod. eq 1, Y (eq 1)
Prod. eq 2, Y (eq 2)
How do you build A2 using Cramers rule in a 2 exponent equation?
ex: 4x + 3y = -23
3x - 5y = 19
[4 -23]
[3 19]
A2 = X from both eq, product from both eq.
How do you finish using Cramers rule once the tables have been populated?
Find the determinants, then,
Find the X and Y values by dividing the determinants
How do you find an X value using a determinate with cramers rule?
X = Det A-1
Det A
How do you find a Y value using a determinant with cramers rule
Y = Det 2
Det A
