Matrix Algebra
Gaussian Elim
Definitions
Properties
Chapter 1 Review
100
Add the two matrices 1 1 1 2 3 4 1 1 2 + 2 5 2 1 2 3 8 0 1
3 4 5 3 6 4 9 2 4
100
Put this matrix in row echelon form 2 6 8 4 12 16
1 3 4 0 0 0
100
A matrix that has its rows and columns switched.
What is a transpose matrix?
100
What is the name of this matrix? 0 0 0 0 0 0 0 0 0
The zero matrix
100
Looks like a first order linear but has a factor of y^n
What is Bernoulli's?
200
Multiply these matrices 1 2 3 * 1 2 0 2 1 2 5 4 2
You can't multiply them.
200
Put this matrix in row echelon form 1 2 3 4 5 6 7 8 9
1 2 3 0 1 2 0 0 0
200
A matrix that equals its transpose.
What is a symmetric matrix?
200
Which is these are valid properties? a) A(B + C) = AB + CA b) A + B = B + A c) A + O = A O is the zero matrix
a) and c)
200
T - Tm = (T(0) - Tm)e^(-kt) is the equation for what?
What is cooling/ heating?
300
Multiply these two matrices 2 1 3 * 1 0 3 2 1 2 3 3 2
13 9 10 8
300
Put this matrix in reduced row echelon form 1 2 8 2 4 16 0 1 4
1 0 0 0 1 4 0 0 0
300
A matrix that has functions for its components.
What is a matrix function?
300
True or False A(BD) = (AB)D
True
300
What are the three elementary row operations?
Switching/ Ri -> Rj Scalar multiplication/ kRi -> Ri Addition/ kRi + Rj -> Rj
400
Multiply these two matrices 1 0 0 4 2 1 0 1 0 * 2 3 4 0 0 1 1 9 3
4 2 1 2 3 4 1 9 3
400
Find the solutions of this matrix 1 2 3 | 4 2 4 7 | 7 2 2 6 | 3
(2, 5/2, -1)
400
A matrix that equals the negative of its transpose.
What is a skew symmetric matrix?
400
True or False (cA)B = B(cA) = c(AB) c is a constant
False (cA)B = A(cB) = c(AB)
400
When solving homogeneous equations, what is the change in variable?
y = vx y' = v'x + v
500
Multiply these two matrices 2 1 0 2 1 0 2 3 * 3 2 0 1 3 0 0
7 4 6 4 3 2
500
Find the solution of this matrix 1 1 1 1 1 | 2 1 1 1 2 2 | 3 1 1 1 2 3 | 2
1 - A - B A B 2 -1
500
Another name for the diagonal of a matrix.
What is a trace?
500
What is matrix A * matrix B in notation form? Hint: It involves a summation and A = a_ij; B = b_ij
Cij = Summation from k =1 to n of (a_ik*b_kj)
500
Give all the change in variables for solving 2nd order differential equations with a missing dependent or independent variable.
Missing dependent (y) dy/dx = v; d^2y/dx^2 = dv/dx Missing independent (x) dy/dx = v; d^2y/dx^2 = v*dv/dy
M
e
n
u