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  1. C

    Find elements of a matrix such that its determinant is zero

    Homework Statement Please see the attached file if my inline insertion does not work. Homework Equations ##det(A)=det(A^T)##[/B] The Attempt at a Solution Since a matrix has a determinant of zero only when it's columns are linearly dependent, we look for a set of points [x1 x2] such...
  2. C

    QR Factorization

    Homework Statement Consider an invertible n x n matrix A. Can you write A as A=LQ, where L is a lower triangular matrix and Q is orthogonal? Hint: Consider the QR factorization of #A^T#. Homework Equations For QR factorization, Q is orthogonal and R is upper triangular. The Attempt at a...
  3. C

    Find all 2x2 matrices X such that AX=XA for all 2x2 matrices

    Homework Statement Find all 2x2 matrices X such that AX=XA for all 2x2 matrices The Attempt at a Solution Let A = a b c d and X = w x y z Then AX = XA ==> aw+by=wa+xc .........(1) ax+bz=wb+xd .........(2) cw+dy=ya+zc .........(3) cx+dz=yb+zd .........(4) (1) ==> by = xc, which...
  4. C

    Orthogonal projection and reflection (matrices)

    Homework Statement [Imgur](http://i.imgur.com/VFT1haQ.png) Homework Equations reflection matrix = 2*projection matrix - Identity matrix The Attempt at a Solution Using the above equation, I get that B is the projection matrix and E is the reflection matrix. Can someone please verify if this...
  5. C

    Transistor and diode circuit

    I just wanted to see if I am understanding this circuit correctly. Let's say the input voltage (V_in) is 0. This means: 1) no current through the 1000 ohm resistor 2) no 0.7V drop from the base to emitter 3) transistor is pretty much off 4) The circuit is open, thus no current goes through...
  6. C

    Circuits with diode

    I have attached the problem along with the answers. I have a question on both of the questions. For the first question, if the diode is ideal, does that mean it's automatically "forward biased?" The problem statement says "assume the diode is ideal (i.e. has a 0V forward bias voltage)...
  7. C

    Should Vout be negative or positive?

    I attached the circuit. I did kirkoff's voltage law (assuming current goes clockwise): -15+5-10,000I-40000I=0 where I=current I=-2*10^-4 A V_out=40,000*-2*10^-4A = -8V The way V_out is shown, it should solve to be negative, correct?
  8. C

    Resistor bands in a circuit?

    Hi guys. I attached a picture of a circuit with 2 resistors in parallel. I want to verify if I'm reading the resistor bands correctly. For the left most resistor, the color gold is the tolerance right? For the right most resistor, the color gold is still the tolerance right? Does the...
  9. C

    Orthogonal vector proof

    Let A be an n × n invertible matrix. Show that if i ≠ j, then row vector i of A and column vector j of A-1 are orthogonal. I'm lost in regards to where to lost. I want to show that a vector from row vector i from A is orthogonal to a column vector j from A. Orthogonal means the dot...
  10. C

    Finding basis for nullspace of transformation

    T: P2 → R (the 2 is supposed to be a subscript) The P is supposed to be some weird looking P denoting that it is a polynomial of degree 2. T (p(x)) = p(0) Find a basis for nullspace of linear transformation T. The answer is {x, x^2} I want to make sure I'm interpreting this correctly. It...
  11. C

    Show this is a basis.

    Show that if S = {v1, v2, . . . , vn} is a basis for Rn and A is an n × n invertible matrix, then S' = {Av1,Av2, . . .,Avn} is also a basis. I need to show that: 1) Av1, Av2,...Avn are linearly independent 2) span(S)=Rn I'm having some problems with this. I see that S'=AS (duh)...
  12. C

    Find Basis for diagonal matrix

    I'm not sure how to start this problem. All i know is a diagonal matrix consists of all 0 elements except along the main diagonal. But how do I even find a basis for this?
  13. C

    Subspace or not?

    Hi. I'm trying to check if my approach is right. The problem is attached. I need to check these: 1) 0 vector is in S 2) if U and V are in S then U+V is in S 3) if V is in S, then cV where c is a scalar is in S The 1st condition is not satisfied right? Since A*[0 0]^t=[0 0]^t≠[1 2]^t?
  14. C

    Linear transformation

    I attached the problem. I'm not sure if I'm misinterpreting the question, but this problem seems really easy, which is usually not the case with my class. for part a) isn't that just the coefficient matrix of the right hand side? This makes A: 1 -2 3 1 0 2 for part b) T(e1)=T[1...
  15. C

    Linear operator

    Hi. I attached the problem and my work. I'm not sure if I did part a) right. In the past problems I've done, they usually provide you with 3 vectors that are linearly independent, thus giving you unique values for C1, C2, C3. The matrix for this one forms: 1 1 1 0 1 3 0 0 0 Which is...
  16. C

    Proving matrices are subspaces

    Hi, I was wondering if someone could check my work for this linear algebra problem. I have attached the problem statement in the file "problem" and my work in the file "work." I would type out my work on here, but I couldn't figure out how to put matrices in a post so I just took a pic of my...
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