MATH 221
quiz6-soln

quiz6-soln - Math 221 Winter 2016 Section 202 Page 1 of 4...

• Test Prep
• 4

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 221, Winter 2016, Section 202 Page 1 of 4 Quiz VI February 16, 2017 No books. No notes. No calculators. No electronic devices of any kind. Name Student Number Problem 1. (8 points) In each case decide whether or not V is a subspace. If V is not a subspace, explain why not. If V is a subspace, ﬁnd a basis for V (no further explanation necessary). 1. V C R3 is the plane through the origin with equation m+3y-2z=0. \} 15 Q Maxim .6 R3. 6}an scum -. (3% (2V2t> ¢Y(. R been (4 V is (SA?) 2. V C R3 is the set of solutions to the system of linear equations 0 2 2x+3y—z x—2y+3x TM Syckm 6“ WWW», lg M): hWoDwm. 1h 2m MW (“.013 .6 NOT a €oluJ‘YM- 90 V docs Mt % 0 umlwh (g), 50 V if NOT asulnspnlz. cl: Rf”. O Math 221, Quiz VI Page 2 of 4 (30qu 3. V is the Md quadrant in R2, deﬁned to consist of all (g) E R2 such that \$20andy30. Y \I is “0% a 940590hz. , x \) («WM 9)) Z/ \i (S doxaL umlw Utd‘tyr aJothm // ‘ . / ® M \I 13 Mi dokﬁ‘ 9(in Suzie” Mu‘hehmimﬂ’ Ry WNWAL (In is iu \J) bu} («\(iA‘ ('1‘) \\\$ Mrs} H“ V 7. gs \} is NOT a hbsfme J R _ 4. V is the range of the linear transformation T : R2 —> R3, given by the formula 31: + y T (I) = x - 2y . y a: + 31 ﬁlm mm? oi may Luca” «Mara-«wh‘ i5 aiming: at \hh‘ipatz. {0 V ii a Su'ﬁfmm at R3 . ’10 ﬁvwi a ham} -‘ V WWI/50f «ii ”“9”“ (3:31) WW 7gp, cut mi MM'VM. W7 (3323: mm . a t w TM“; X“, I U [MW WBM‘WQ (‘7, (3;), ('15) . 50 V: 9P“ {Ell/J?) . (”W )(U «m M Scalar mulh'du J 2ch 0W, +sz ' I “Na-wt) {hob/MM) aw, hunt 45W“ G 4955'} ’3 V w W [W427 q gintt Math 221, Quiz VI Page 3 of 4 Problem 2. (8 points) It is given that 3494—3)) is a basis of R2. Note that the two vectors in B are orthogonal to each other. Denote the stande basis of R2 by S. ' Let T : R2 —> R2 be orthogonal projection onto the line L = span (—43) . 1. Find the matrix [T] ,5 of T with respect to the basis 13. 2. Find the matrix P such that [015 = P [1313, for all vectors 17 E R2. 3. Find the matrix Q such that [ﬁg = Q [1713, for all vectors 27 E R2. ’1’) 4. Find the standard matrix [T]5 of the projection T. @ (P is “a Ira-NSX'M “h”; "V, “WM“: me lea ban? WM (P :(QtS ‘1) - Lt 3 - _I_ “l '5 ® Q=l> ‘ = lt‘+‘1(-’> LA ' 75 (,3 LA ® [’1 = ? "= “f “3 0 ‘. 3 l), [T15 P (I); a) (o TBKK: Lt) :10,3L{3-Lq-‘7_ 2.; 0” 4% 'z‘m‘b. Math 221, Quiz VI zc—BL m um) ( L -2:~‘f8) 7,5’ (as 4- 6% Page 4 of 4 %c(flf§\= (Ci) / ...
View Full Document

• Spring '10
• PETERSEN
• Linear Algebra, doxaL umlw Utd‘tyr, Quiz VI Page, Ry WNWAL

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern