Tutors Answer Your Questions about Linear Algebra (FREE)
Question 36646: This is my second and last question. This is not in a textbook.
a.)Let T be a linear operator on V. SHow that if (Tu|v)=0 for every u,v in V, then T is the zero operator on V.
b.)Prove the Generalized Pythagorean Theorem: Suppose {v1,v2,...,vn} is an orthogonal set of vectors. Then ||v1+v2+...+vn||^2=||v1||^2+...||v2||^2+...+||vn||^2
For (a.) I think you fix u and get it, but I don't understand how.
For (b.) Do I only have to do this:
||v1+v2+...+vn||^2=(v2+v2+...vn|v1+v2+...+vn)
=(v1|v1)+(v2|v2)+...(vn|vn) since the vectors are orthog.
=||v1||^2+...||v2||^2+...+||vn||^2
Is this all i have to do or is there more steps in there?
Click here to see answer by venugopalramana(3286)  |
Question 39593: Question; Determine whether or not W is a subspace of R3, with justification (general proof).
W={(x,y,x+y); x and y are real)}. I have a trouble in proving(in general, not specific numbers) the closure axioms(addition and scalar multiplication). Please help!
Click here to see answer by cininnatus(12) |
Question 39572: Proof of a singular matrix:
I need to show (in general) that either matrix A is "singular" or "A^2 = A^(-1)". A is an n*n square matrix such that A^4 = A. I want to know how to do this problem and what happens if the exponent values are different.(for example, odd number exponents?)
Click here to see answer by venugopalramana(3286) |
Question 40449: I posted a question just a few minutes ago and Nate answered it but he didn't exactly answer what I am looking for. My slope is 2/3 but how do I get this into y=mx+b format. The question is Line 2 is perpendicular to a line that passes through the points (4,-3) and (-2,6). I know that the slope is 2/3 but how do I get this into y=mx+b?
Click here to see answer by smik(40) |
Question 40520: Last one:
Let T:R^n --> R^m be a linear transformation, and let {v1, v2, v3} be a linearly dependent set in R^n. Prove that the set {T(v1), T(v2), T(v3)} is linearly dependent.
I have proved it closed under addition and scalar multiplication, but am not sure if this is correct? Should I be looking at the trivial solution?
Thank you!
Click here to see answer by kev82(148) |
Question 42660: Give the equation or other information on for a parabola, find the matching discription or graph.
f(x)-a(x-h)2+k the 2 after ) is square
a is less than 0
h is equal to 0
choices:
a. the graph of f(x) does not intersect x-axis
b. you can not tell from the information given
c. the graph of f(x) interescts the x-axis at one point
d. the graph of f(x) intersects the x-axis at two points
Click here to see answer by Nate(3500) |
Question 42821: The perimeter of a rectangle is given by p=2w+2h where w is the width and h is the height. Find the height if the perimeter is 52 inches and the width is 14 inches. I have worked the question out and came up with 13in. Would like to know if this is right. Thanks again for any help.
Click here to see answer by josmiceli(9664)  |
|
Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510
|
