Recent content by Tonyt88

Homework Statement V = span(S) where S = {(1, i, 0), ((1-i), 2, 4i)}, and x = ((3+i), 4i, -4) Obtain the orthogonal basis, then normalize for the orthonormal basis, and then compute the Fourier coefficients. Homework Equations v2 = w2 - (<w2,v1>)(v1)/(||v1||²) The Attempt at a...

Basically, I'm having difficulty understanding the concept of stability, I have reread the chapter in my book various times, but to no avail. Can anybody give a very brief overview in simplified terms as to what determines whether or not a matrix is stable. Thanks.

Homework Statement Consider a symmetric n x n matrix A with A² = A. Is the linear transformation T(x) = Ax necessarily the orthogonal projection onto a subspace IR^n? Homework Equations The Attempt at a Solution No idea what thought to begin with.

Homework Statement Consider a dynamical system x(t+1) = Ax(t),, where A is a real n x n matrix. (a) If |det(A)| > or equal to one, what can you say about the stability of the zero state? (b) If |det(A)| < 1, what can you say about the stability of the zero state? Homework Equations...

Homework Statement Express the plane V in 3 with equation 3x1+4x2+5x3=0 as the kernel of a matrix A and as the image of a matrix B. {Note: the 1,2, and 3 after the x are subscript} Homework Equations The Attempt at a Solution Would the relevant matrix just be a [3 4 5] with an...

Homework Statement Give an example of a linear transformation whose kernel is the line spanned by: -1 1 2 in lR³ Homework Equations The Attempt at a Solution Would: 1..(-1)...0 0...0...0 0..(-2)...1 be a solution?

It's reduced row-echelon form, but nevermind, I got the answer, though thanks for the help.

Homework Statement Consider a matrix A, and let B = rref(A) (a) Is ker(A) necessarily equal to ker(B)? Explain. (b) Is im(A) necessarily equal to im(B)? Explain. Homework Equations The Attempt at a Solution I feel confident saying yes for (a) and no for (b), and what I can...

To reduce it would you switch row 2 and 3?

Homework Statement Determine which of the matrices below are in reduced row-echelon form: a) 1_2_0_2_0 0_0_1_3_0 0_0_1_4_0 0_0_0_0_1 b) 0_1_2_0_3 0_0_0_1_4 0_0_0_0_0 c) 1_2_0_3 0_0_0_0 0_0_1_2 d) 0_1_2_3_4 Homework Equations The Attempt at a Solution Okay...

Sorry I had only put it in the title of the thread. Find all solutions of the linear system. Describe your solution in terms of intersecting planes.

Homework Statement x + 4y + z = 0 4x + 13y + 7z = 0 7x + 22y + 13z = 1Homework Equations The Attempt at a Solution x + 4y + z = 0 - 3y + 3z = 0 -6y + 6z = 1 x + 4y + z = 0 -y + z = 0 -6y + 6z = 1 Then whichever way I solve it I have 0=1 or 0=1/6, so where to go...

Hmmm, so am I not supposed to find a derivative somewhere, or?

Homework Statement Consider a planet with uniform mass density p. If the planet rotates too fast, it will fly apart. Show that the minimum period of rotation is given by: T = (3 pi)^(1/2) ...(G p)^(1/2) What is the minimum T if p = 5.5 g/cm^3? Homework Equations T = 2 pi r...

Stoke's Theorem Homework Statement F(x,y,z,) = (3x+y)i - zj + y²k; S = the union of the cylinder {(x,y,z) : x² + y² = 4, 2 < z < 4} and the hemisphere {(x,y,z) : x² + y² +(z-2)² = 4, z < 2}, oriented by P |--> n(P) with n(0,0,0) = -k Use Stoke's Theorem to evaluate the double derivate of...