# rows

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. ### Finding critical rows without the need to construct the whole table?

I'm trying to use the truth table to know whether an argument is valid or not, I have 5 premises and 5 variables which makes it really difficult to construct the whole table as I will need 32 rows.. I do remember that there is a way in which I can use by finding the critical rows only without...
3. ### 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...
4. ### Find the number of rows of seats

A multimedia library as 108 seats, which are all arranged in rows. The number of seats in each row is 3 less than the number of rows. How many rows of seats are in the library? The answer appears to be 12 but I can't figure out how to set up an equation with variables and solve for this.
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. ### Character table: sum of elements in rows

Prove that the sum of elements in any row of the character table of a finite group G is a non-negative integer. This can be proven by considering the character of the permutation representation acquired by letting G act on itself by conjugation. I don't see the significance of the permutation...
7. ### next two rows

give the next two rows 1 11 21 1211 111221 312211 13112221 1113213211 31131211131221 ------------------- -------------------
8. ### linear combination of rows

Let a be a 1 x n matrix and B an n x p matrix. Show that the matrix product aB can be written as a linear combination of rows of B where the coefficients are the entries of A. I don't get how you can have a combination of rows.
9. ### n rows determinant value 6

\begin{vmatrix} 1 &. &. &. & &1 \\ 0&1 & & .& . & 1\\ 1& & 2& & &1 \\ .& & & 3& & 1\\ .& & & & . & 1\\ 1& & & & & n-1 \end{vmatrix}=-(n-2)! is it true
10. ### 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...
11. ### critical rows - what if there are none?

Why is an argument valid if there are no critical rows? I know that if all premesis' are true (this forms a critical row), then the conclusion must be true to make the argument valid. I understand that if all premesis' are true, and a conclusion is false, then the argument is invalid. but why...
12. ### 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?
13. ### How to solve a system of linear equations when there are less rows than variables?

I took a year off from Math before deciding to major in it, so I'm a little rusty. I've come to a point in a problem where I have 2 linear equations: -2a+3b+9c=0 and -2a+5b+4c=0 I'm unsure of how to solve these 2 equations. I can cancel out one of the variables, but after than, I don't know...
14. ### 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...
15. ### Linearly independent rows

Let A be an n x n matrix. How do you show that the rows of A are linearly independent if and only if the columns of A span R^{n}?
16. ### how can you plant 10 trees in 5 rows of 4 trees each?

how can you plant 10 trees in 5 rows of four trees each? 2) you have a 5-liter bucket and a 3-liter bucket and NO OTHER MEASURING device . using these buckets how can you measure out exactly 4 liters of water.
17. ### MATLAB: reading multiple rows as one

I'm having a problem reading more than one line of data at once. I have thunderstorm cloud data in the form of a .txt file. Every row of data consists of different variable for up to six clouds. For example. cellnum = number of clouds latitude longitude area temperature cooling rate The...
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?
19. ### trigonometry and rows

I need to prove that: sin x + sin 2x+ ...........sin nx = (sin nx/2 * sin (n+1)x/2) / sinx/2 it is specified that sin x/2 is not 0 ,and that n is >=1 I used various trigonometry theoremes but i just cant find the algoritamto solve my problem so please if anyone knows how to...