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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
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5
3. {shw 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 + 2.225.53 " 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.?
$5
5;} “5’
gm. f2:
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W5 j (9 MATH 115, Midterm Page 5 of 11 I Name: MATH 115, Midterm I Page 6 of 11 Name: [6] 5. Find the matrix A Where MATH 115, Midterm ‘ ‘ Page7of11 _ "Name: 1 D *2
6. Let A 2 D '—2 2
_ 1 '2 —2 [3] (a) Find det(A). WW/J giﬁgéﬁ [2] (b) Is A invertible? Explain.   w» w ' 7 5M 4 J I f; h. f ﬁg m 4%,, gJ x ?" MATH 115, Midterm I Page 8 of 11 Name: [4] 7. Let S, T i R2 —> R2 be two linear transformations deﬁned as foliows:
3WD = [2m] and TU$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
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:a =
2‘
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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,
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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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 Fall '07
 DUNBAR
 Linear Algebra, Algebra

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