Midterm1sol

Midterm1sol - MATH 115, Midterm Page 2 of 11 Name: [3] 1....

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Unformatted text preview: MATH 115, Midterm Page 2 of 11 Name: [3] 1. (a) Find the parametric equations of the line containing tgle points‘ (1, 2, —1) and (2, 1,1) ’2 § 5 3. {sh-w a?“ f the} “'1' age! 5 [3] (b) Find the equation of the plane perpendicular to the line in part (:1), containing the point (1,2, ~1). - MATH 115, Midterm ' Page 3 of 11 Name: [4] 2. (3.) Find the general solution to the followifig system 33 + 2.22-5.53 -" 21:4: 5 361+ 232+$3 + $4 = 0 MATH 115, Midterm Page 4 of 11 ' Name: [2] 3. (a) Write the system 4x+y = 11$+3y=2 in the form of a, matrix equation An? = ._ 3.? $5 5;} “5’ gm. f2: _: 4* W5 j (9 MATH 115, Midterm Page 5 of 11 I Name: MATH 115, Midterm I Page 6 of 11 Name: [6] 5. Find the matrix A Where MATH 115, Midterm ‘ ‘ Page7of11 _ "Name: 1 D *2 6. Let A 2 D '—2 2 _ 1 '2 —2 [3] (a) Find det(A). WW/J gifigéfi [2] (b) Is A invertible? Explain. - - w» w ' 7 5M 4- J I f; h. f fig m 4%,, g-J x ?" MATH 115, Midterm I Page 8 of 11 Name: [4] 7. Let S, T i R2 —> R2 be two linear transformations defined as foliows: 3WD = [2m] and TU$D=W1 1! ~26 I. y - 11 Find the matrix of the transformation 5' o T. Hence find 3 o T 2 . MATH 115, Midterm ‘ 8. Given a. point P(2;1,y1_) E R2, let T [2] [2] [1] Page 9 of 1 Name: 5'31 y be the point on the line y = a: closest to P. 1 . [3.) Draw a. sketch showing how T acts on vectors in RF. ‘3 ff ow £54313} (13) Find the matrix of the linear transformation T. (There is no need to Show that T is linear) J L 9 i‘. :a = 2‘ "a gs {is i i RAE" / ._ i ‘7ng fairsffi a, W . L W 7/91“ MATH 115, Midterm ‘ Page 10 of 11 N eme: [8] 9. Determine if the following statements are true or false. If the statement is true, prove that it is true. If it is false, prove that it is false, (8.) If A and B are invertible, then A + B is invertible. (b) If A is invertible and symmetric, then A‘1 is symmetric. ‘3‘ refit?!“ 4,... m *3 very . =1“; _ . _. W, = . I, if 5,! 3 mum}; Ill ; If ’ , I I; 3 wall"? 5;;- ;. e ’ ' R” I, , i at“? a t i as ,e, .535 is.» i‘ .‘g .iQ-Jfg WP r s. “Wiring 23??" (c) If a system has 4 equations and 5 unknowns, then the solution must contain exactly one parameter. ' ' (d) The function T : R2 -+ R2 given by T = gay] is linear. ...
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Midterm1sol - MATH 115, Midterm Page 2 of 11 Name: [3] 1....

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