matrix

1. Advanced Matrices and Cryptography Question Help

Hello, I was stuck on the following question. 'Your task it to crack the following code and find the encrypted word. To make your task easier, the following information about the encoding matrix is given: Position 1,1 in the encoding matrix is an even number. The decoding matrix only contains...
2. Negative of matrix associated with bilinear map for odd dimension

Hiya, Hate to ask a question without essentially any work on it, but I have no idea how to prove this. The question is : Let $F$ be the matrix of a nonsingular bilinear form $f$ on a real space of dimension n. Prove that for odd $n$ the matrix $−F$ is not the matrix of $f$ in any basis of $V$...
3. Find Determinant of the Matrix

Hi! My HW task is to find determinant of given matrix. I tried to do elementary row operations, but did not get anything. How to get rid of ? Answer should be 0 for p>2.
4. True or false span questions

Hi, Could someone please help me with the two questions below? 1. I think that it would be false but I can't really tell. 2. n x (n+1) matrix is merely suggesting that there is one more row than column. I don't see any reason here why Ax = 0 would not be solvable. Therefore the question...
5. Linear independence and dependence

Hi, I'm trying to understand linear independence from a graphical standpoint: The reasoning behind why a is linear independent is because the vectors do not lie on the same plane when placed with their initial points at the origin - I struggling to see this. Can someone please explain? b...
6. Independent v.s. dependent columns

Hi, I'm lost with this image: Can someone please explain the description of Figure 4.7? How is a1, a2, and a3 not in a plane while c1, c2, and c3 in the same plane? I struggling to find the reasoning behind this. (Sorry I forgot to convert the "1" in "a1" and the "2" and "a2" etc as...
7. General solution in vector form

Hi, I'm currently trying to understand the general solution to a system of linear equations in vector form. Let's say that when the system is in row reduced matrix form, there is a column will all zeros. According to the image that I took from a textbook, a zero column would suggest the...
8. Solutions of 3 x 3 matrix

Hi, I hope someone can help (urgent). Let's suppose I have a system of three equations in three unknowns. Can such a system have exactly 2 distinct solutions? I would think that it is possible, but only in the event where the third unknown gets cancelled out during row reduction operations...
9. Graphical analysis of linear systems

Hi, I'm in the midst of solving the question below: I am pretty certain that b is a solution - based on the parallelogram rule (it seems to be a linear combination of c1v1 + c2v2 + 0v3). In terms of the type of solution... I'm not really sure. One thing that I do notice, is that one of...
10. Geometric description of span

never mind ignore this post
11. Determining inconsistent matrix

Hi, I hope someone can help. Lets suppose a system of linear equations has a 3 x 5 augmented matrix whose fifth column is a pivot column. Is the system consistent? I feel that it wouldn't matter if the fifth column is a pivot column since that column represents just constants in the equations...
12. Determining inconsistent system

Is there anyway to determine at face-value whether or not this linear system of equations is consistent or not? Consistent being that it has at least one solution. For example... I would really appreciate help!!! - Olivia
13. Determining that the system has no solutions

Hi, I hope someone can help me with the question I have. The image I attached below is me trying to solve a systems of linear equations (the system is in the top left of the image). I struggled to find a solution to this problem... and it turns out that apparently there are no solutions. I...
14. Numerical methods -finding matrix inverse

Hello new to the forum so if this in the wrong topic I do apoligise. im struggling to work out why to find the inverse of upper triangular and lower triangular matrix of a nxn matrix the operation order is 0(N^3). i get that for a normal NxN matrix, using gauss elimination we get 0(N^3) but...
15. Condtion number to estimate the upper bound for the relative error

Hi I have been attempting the question as shown above. I did (3Bi) and calculated the condition number for the Frobenius norm to be 526.1588 I do not know how to use this in part (ii) to calculate the upper bound for the relative error. Can anyone point me in the right direction :)
16. Linear Algebra Identity Understanding

I have a solution here that I don't quite understand. Q: Show that if a square matrix A satisfies the equation A^2+2A+I=0 , then A must be invertible. A: A^2+2A=-I -A^2-2A=I I got this far on my own, but the next step confuses me... A(-A-2I)=I I get that if A^-^1=(-A-2I) then A*A^-^1=I...
17. How to solve for two variables in a 3x3 matrix?

Hi. I have this question on my Pre-Calculus homework that honestly I have no idea what to do for. We never went over this specific type of problem in class (go figure) and I'm unable to find anything else helpful on the internet. The problem is to solve for the two variables in this 3x3...
18. How to transform multiple 3d points by different distances with a matix calculation?

If I have a 3d point $(x,y,z)$ and I want to translate it by a vector $v$, I can just multiply it by a matrix as shown here https://en.wikipedia.org/wiki/Translation_(geometry) Also I know that if I want to translate n points at the same time, I can just combine it into \$ \begin{bmatrix}...
19. matrix to power 100 with cayley hamilton

Hi! i have the matrix A= ( 1 1 -1 -1 -1 0 0 -1 0 ) The characteristic polynomial is -A^3 + A - 2 I have to find A^100 with Cayley Hamilton Can anybody help me?
20. Top m eigenvectors of positive semidefinite matrix of dimension N and rank m<<N ?

Consider a real symmetric and positive semidefinite matrix of dimension N~10^5 and rank m~2000. What is the most efficient algorithm for determining the top m eigenvectors?