2.4 Matrices and Systems of Linear Equations Flashcards
(13 cards)
gaussian solving equations
What is reduced echelon form?
Any row containing only 0s comes below any row not containing only 0s
The first non zero value in any row is 1, and comes to the right of the first 1 in the row above it
Each leading 1 is the only 1 in the column containing it
What is an n dimensional real vector and how can they be written
It is a n x 1 matrix (1 wide, n down)
R (real) ^n
or like this (1, 3, 5)^T
for a pair of vectors u and v, the dot product u.v also equals what?
u^T X v
u transposed, matrix multiplication with V
What is the determinant of
1 2 4
3 1 -1
2 5 6
A system of equations has a unique solution if what?
The matrix’s determinant is non-zero
|AB| =
|A| X |B|
How do you know if a matrix is invertible
If its determinant is non-zero
What makes a square matrix a lower triangular?
If all entries above the diagonal are 0’s.
when scaling a vector image by alpha, what is the change in screen area?
the change in screen area is alpha^2
if an image is stretched by
ax
y
what is the change in screen area
a
when rotating a vector image anticlockwise, what is the rotation matrix?
cos(theta) -sin(theta)
sin(theta). cos(theta)
what matrix should you apply to achieve a transformation of
stretched horizontally by scale 2
and rotated 90* AC
- -1
- 0
