# columns

1. ### Determinant with n rows and n columns

If i try to expand any of the rows or columns it just gets more complicated.
2. ### The rows of this unitary matrix form an orthonormal set but the columns don't. Why?

The rows of this ( {{1/3 - 2/3i,2/3i},{-2/3i,-1/3-2/3i}} - Wolfram|Alpha ) unitary matrix form an orthonormal set but, the columns of A do not form an orthonormal set despite this ( https://en.wikipedia.org/wiki/Unitary_matrix#Equivalent_conditions ) Wikipedia article saying that they...
3. ### Null space for Matrix with similar columns

Hi, I just read that the null space for the following matrix [1 0 1; 5 4 9; 2 4 6] is the line of all points x = c, y = c, z = -c. I was wondering what the null space for the matrix with three similar columns would be e.g. [1 1 1; 0 0 0; 0 0 0] (c, -c, 0), (-c, 2c...
4. ### Definition of determinant and connection to linear dependance of columns

Hi, In my book on linear algebra (first year university) the author starts off explaining the concepts of determinants by focusing on dimensions n<=3, giving geometrical definitions of area and volume. Then he goes on to explain that if the area/volume given by the columns vectors is zero...
5. ### Finding recessive rows and columns in a matrix

Ok, I have been looking for 2 days on the web before posting and I think the web has only confused me even more as I have got into text books like linear algebra for dummies and such. Ok I will explain what I am trying to do and hopefully someone can tell me how to do this. So in Linear...
6. ### show columns are linearly independent if homogeneous system has only trivial solution

Let A be an m x n matrix. Show that the columns of A are linearly independent iff the homogeneous system Ax=0 has just the trivial solution. I think I need to use the fact that a homogeneous system of n linear equations in n unknowns has a nontrivial solution iff rank(A) < n
7. ### linear dependence of matrix columns

if i have a m x n matrix (call this matrix A for arguments sake) and an n x p matrix (call this matrix B) how would i prove that, if the columns of B are linearly dependent, then so are the columns of AB? i have been looking at the definition for linear dependance but I have been struggling...
8. ### Boolean Matrix : Minimum number of columns

Hi all, I was trying to solve a programming problem.. and it narrowed down to this question. I am given N and M (both non-zero integers and M<N).. I need to construct a boolean matrix such that 1. Number of rows have to be equal to N 2. Every column must have M 1's exactly(rest 0) 3. No two...
9. ### adding rows and columns....

i heard about this problem,but i am not sure if its correct.anybody who knows this problem may please correct the problem....however it may be right also (Itwasntme) so here it goes: consider an 8x8 chessboard.now every squares of the board is filled with either -1 or +1.the product of each rows...
10. ### Question regarding determinants and switching columns of square matrices

A is a square matrix length n and b is a vector in R^n. For every k=1,2,...,n A_k is the matrix that is received from A after switching the k column with vector b. Given, detA=0. Prove that if detA_1 \neq 0 then there is no solution to Ax=b. This is what the question means if it was...
11. ### Creating 2 columns in latex document

I'd like to create something that looks like the pdf document below. The only thing is, I don't think I can do 2 columns, as I would like normal text to go under that. I'm thinking of maybe a table, but I've never done a table before in LaTeX. I think this might do the job. Could someone tell...
12. ### if a martix has an inverse why must the columns be linearally independent?

From wikipedia "Let A be a square n by n matrix over a field K (for example the field R of real numbers). The columns of A are linearly independent." why does this work?
13. ### Smallest number of linearly dependent columns?

I have a known parity check matrix H (5x3) of some unknown code C in which I want to find the minimum distance of the code. I understand from reading that to determine the minimum distance I can find the smallest number of linearly dependent columns in the parity check matrix, but...
14. ### Columns in a LaTeX File

I'm trying to write a LaTex file and i want to get divide what i have into two columns on one page. But i'm not sure how to format it. Any ideas?
15. ### Figuring out rows and columns after matrix multiplication

Suppose A is a n x k matrix and you have A(A^TA)^{-1}A^T. All that is equivalent to I, but how many rows does I have? Is it n or k, and what is a quick way to figure it out?
16. ### multiplying columns and rows

My professor drew many pairs of matrices on a sheet of paper. He then asked "Which ones are in illegal positions?" I believe I already know this but I want to make sure: You can't have rows on the left, and columns on the right? However, the other way around is fine. Just want to make sure...
17. ### Columns width under multicolumn

Good afternoon everybody, I am a begineer in Latex and I have some trouble setting column's width in a Latex document. I have double columns under which I would like the columns to be split evenly (50% of the double column each) but I juste don't understant how to get this result. Here is a...
18. ### Students in rows and columns

Thirty-five student are seated in five rows and seven columns. Is it possible for the student to change seats if every student much move exactly one seat to the left, right, front, back?