Explain
Describe:
Parametric form
What is
The general solution to the system using parameters such as r, s, t
r, s, t, epsilonbbb"R"
How many types of solutions are there? Name each.
What is
3 different solutions:
- Unique / independent
- No Solution
- Infinitely many solutions / Dependent
If
A=[[8,0,2],[3,1,7],[1,2,3]]
find
A^-1
What is
A^-1=[[11/78,-2/39,1/36],[1/39,-11/39,25/39],[-5/78,8/39,-4/39]]
Find the determinant of the following
[[6,5],[2,1]]
What is
-4
How do you find the unit vector of
vecv
What is
vecu=1/normvecvcdotvecv
How do you know you are working with a homogenous system?
What is
When your system is equal to all 0's
or
Your constant matrix is all 0's
Looking at the augmented matrix why are there infinitely solutions possible?
[[1,-2,3,-2,| ,0],[-3,6,1,0,| ,0],[-2, 4,4,-2,| ,0]]
What is
There are more rows than columns in the matrix, causing a free variable.
If
A=[[8,0,2],[3,1,7]]
"Find"" " A^T
What is
A^T=[[8,3],[0,1],[2,7]]
Name the process used to find the determinant of a matrix larger than a 2x2.
What is
Cofactor Expansion
Find the norm of the following vector.
norm(vecv)=2[[3],[6],[2]]
What is14
If A is an nxn matrix with n distinct eigenvalues, then A is...
What is
diagonalizable and P & D exist
If a system has 6 columns but is of rank 2 how many basic solutions exist?
What is
4
(by Thm 1.3.2)
Find the inverse of the following matrix
[[1,-1,2],[0,1,1],[1,0,0]]
Answer in fraction form.
What is
[[0,0,1],[-1/3,2/3, 1/3],[1/3,1/3,-1/3]]
Find the determinant of
B=[[2,0,0,0,0],[0,3,0,0,0],[0,0,6,0,0],[0,0,0,1,0],[0,0,0,0,4]]
What is
144
Let
vecu=[[4,2,9]], vecv=[[3],[2],[2]], vecw=[[1],[0],[2]]
Find
vecucdot(vecv-vecw)
What is
12
What equation is used to find the eigenvalue(s) of a matrix?
What is
det(lambdaI-A)=0
Solve the following system
{(x,-,3y,+4z=,7),(,,y,+2z=,2),(,,,z=,5):}
What is
x=-37, y=-8, z=5
"If"" " A=[[3,4,2],[1,3,2]] " ""&"" "B=[[2,4],[4,1],[0,3]]
"Find"" "AcdotB
What is
[[22,22],[14,13]]
What Row Operation can you preform that will not change the determinant?
What is
Multiplying by a scalar and adding to another row.
ie:
kR_1+R_2->R_2
If
vecu=[[3,1,1]] " "&" " vecv=[[2,2,5]]
find
vecuxxvecv
What is
vecuxxvecv=[[3,-13,4]]
What equation is used to find the eigenvector(s) of a matrix?
What is
(lambdaI-A)vecx=0
What is the rank of the following matrix
C=[[0,4,4,-4,4],[1,-1,-3,10,-4],[0,3,4,-5,1]]
What is
Rank 3
Find the elementary matrix E such that B=EA, where
A=[[1,2],[-1,1]]" ""and"" "B=[[1,2],[0,3]]
What is
E=[[1,0],[1,1]]
To diagonalize matrix A you would need to solve
P^-1AP=D
How do you construct P and D?
What is
P= [vecx_1,vecx_2,vecx_3,...]" " "&"" " D=[lambda_1, lambda_2,lambda_3]
"where"" " vecx_n" " "are eigenvectors"
Find the projection of
vecu=[[3],[-13],[4]]" ""on"" " vecd=[[1],[-1],[3]]
What is
proj_vecdvecu=(vecucdotvecd)/normvecd^2vec d=
28/11[[1],[-1],[3]]"or" [[28/11],[-28/11],[84/11]]