Recent content by cal.queen92

Definitely over thinking this, think I just had a light bulb. Thank you guys for your time and patience!

I'm not sure... I think I'm really just having trouble figuring out with this question is asking. From what I understand, together, we did the proof that was required (b=0). Is that all that is being asked for?

hehe Okay, I understand, but... Just one last question: Does what we did here (proving that b = 0 makes the transformation linear) ALSO define the function as asked in the first part of the problem statement?

You have helped a lot, thank you! The rest of my question is really about the first part of the statement: "Suppose A is an mxn matrix and b is a vector in R^m. Define a function T:R^n --> R^m) by T(x) = Ax + b." Perhaps I'm over thinking it, but what does it mean to define a function in this...

Okay, I made u & v zero vectors so that T(u+v) = T(u) + T(v). (T is linear) Now, one rule I have says that to define the function (or for T to be linear), T(0) = 0 (has to be so) So this means that if T(u) = A(u) + b, then b has to be a zero vector as well right? Does proving that a...

Thank you! So I gave numerical values to the matrix A, & vectors b, u &v (making b a zero vector) and was able to conclude that T(u+v) = T(u) + T(v). Since I made b a zero vector, this helps me with the second part of the problem. However, how can I connect this to the first part of the...

Homework Statement Suppose A is an mxn matrix and b is a vector in R^m. Define a function T:R^n --> R^m by T(x) = Ax + b. Prove that if T is a linear transformation then b=0. Homework Equations For the second part of the question, a transformation is linear if: 1) T(u+v) = T(u) +...

I also tried first obtaining the diagonal 1's that I need, but it gets too messy!

Great! thank you, I did that, now I have a leading one in the second row. I;ve tried the next step two ways, 1) eliminate second entry of first row 2) make all entries below leading one of second row 1's But neither helps me move forward

Homework Statement Given the following vectors: (don't give values to variables) V0 = (1 1 1 1) V1 = (x1 x2 x3 x4) V2 = (x1^2 x2^2 x3^2 x4^2) V3 = (x1^3 x2^3 x3^3 x4^3) a) prove that the 4x4 matrix A, whose columns are the vectors above, row reduces to the 4x4...

Homework Statement indefinite integral: dx/(x*sqrt(9+16x^2)) Homework Equations Trig. Substitutions or parts?? The Attempt at a Solution I tried using integration by parts but its got pretty messy...it also resembles a tan trig substitution, but it's within a square root. I'm...

Thank you! That was it, didn't take the proper dv -- took x^7 as oppose to 1/x^7 giving x^-7. Perfect!

Homework Statement The problem is divided into two sections: a) does the improper integral: 2ln(x)/x^7 (from 1 to infinity) Converge or diverge? If it converges, to what value? b) Determine whether the series: sigma n=1 to infinity (2ln(n)/n^7) converges or diverges. Homework...

Thank you!

Homework Statement A man of 80.0 kg is standing in the cabin of a Ferris wheel of radius 30.0 m rotating at 1.0 rpm. What are the forces that the feet of the man exert on the floor of the cabin when he reaches the highest point and the lowest point? Homework Equations Newton's Second...