Recent content by brownman

How come a square matrix has eigenvalues of 0 and the trace of the matrix? Is there any other proof other than just solving det(A-λI)=0?

Oh... Okay I get it now. If I use the matrix 0 0 0 1 = A and 0 0 0 0 = A2 The nullspace of A2 has infinite solutions and the nullspace of A will have at least one x value that will have to be zero in order for it to be a valid equation, so...

Homework Statement Say that A is a square matrix. Show that the following statements are true, or give a counter example: a) If x is in the nullspace of A, then x is in the nullspace of A2 b) If x is in the nullspace of A2, the x is in the nullspace of A. Homework Equations The...

If this were the reduced row echelon form of an augmented matrix, 1 2 0 1 1 0 3 0 0 1 2 1 0 1 0 0 0 0 0 1 2 0 0 0 0 0 0 0 What is the form of the following answer given, and how can I understand it? (x1; x2; x3; x4; x5; x6) = (3; 0; 1; 0; 0; 2)+ t(1; 0; 1; 0; 1; 0)+ s(1; 0; 2; 1; 0...

Okay the combined definitions from all of you seem to make a general sort of sense, thank you for the help guys :)

I'm looking for the deeper meaning behind this law/theorem/statement (I don't know what it is, please correct me). My textbook just told us a matrix is not invertible if the determinant is zero.

Oh yeah there is the trivial solution. Thanks for the help in clearing it up :)

Homework Statement If A2 is a zero matrix, find all symmetric 2x2 nilpotent matrices. Homework Equations The Attempt at a Solution So if A2 is nilpotent, then [a,b;c,d]*[a,b;c,d] is equal to [0,0;0,0]. Since A is symmetric, b=c. Multiplying the two matrices, I get [ aa...

I believe I made a typo here in entering, as I still return 10\pm8\sqrt{2} as the roots. The problem has been solved though, my instructor sent an email regarding the error with the homework system. Again, thank you for your help!

I've left it in MATLAB notation, so the semi colons indicate a new row and spaces mean the next entry is in the next column. Thanks for helping me clear that up, I used the quadratic equation to solve for k but I got the roots 10±8\sqrt{2} which are apparently incorrect. Perhaps it's at this...

Homework Statement Find all values of k, if any, that satisfy the equation. [2 2 k]*[1 3 0; 3 0 5; 0 5 -1][2 ; 2 ; k]=0Homework Equations The Attempt at a Solution Multiplying the two matrices on the right [2 2 k] * [8 ; 6 +5k ; 10-k]=0 Multiply again [ 16 + 10+12k + 10k-k^2]=0 I'm...

Oh okay, that makes sense, thanks for the help :).

Homework Statement Solve the inequality -9 < 1/x A simple inequality, I can see the solution is just x < -1/9 but I can't prove it at all. The Attempt at a Solution -9 < 1/x -9x < 1 x > -1/9 Any helpful rules I am forgetting about inequalities? This was a problem in a review...