Eigan Values, Eigan Vectors-Linear Algebra-Paper Solution, Exams of Linear Algebra

Download Eigan Values, Eigan Vectors-Linear Algebra-Paper Solution and more Exams Linear Algebra in PDF only on Docsity!

PAKISTAN INSTITUTE OF ENGINEERING AND APPLIED SCIENCES 2"4 Semester, BS Mechanical _ LINEAR ALGEBRA SESSIONAL TEST-II Time Allowed: 1 hour 30 minutes Total Marks: 25 Date: May 26, 2011 1. For what value(s) of 2 will y be in span {v,, vs, ¥; dif 1 5 3 -4 y -|-1),% -|-4], 4 =] 1 Landy =] 3 -2 -7 0 h 2. Determine if the following vectors are linearly independent 0} | 0 -3 OL) 5 || 4 2\|-8 1 3. Find the value(s) of # for which the following vectors are linearly dependent 1 3 -1 -1],)-5),] 5 4 7 3 A ¢ =| 2] and define a transformation T: R?-—» R? by 5 a. Find an Xin R? whose image under 7 isd. b. Determine if cis in the range of the transformation T . = [1] — fo] — [2] —_j|-1 > 5. Let e, 0} (i) yy -[:} ya = I< and T: R? —» R? bea linear transformation that maps ¢, a a 5 x, into y, and maps @, into y, . Find the images of A and] “7 _ X * 3x, +X, 6. Let r( =| 5x, + 7x, x, +3x, Show that T is a one-to-one linear transformation. Does T map R? onto R?? Show all the details. 7. let? : R? —> R?bea linear transformation such that T(x,,x) =(x, ~ 2x, ,-%, + 3x,3% —2x,). Find such that T(F} = (-14,9) Page 1/1 docsity.com