LINEAR ALGEBRA EXAM 4 version 1 name: 1. Suppose A is a square real matrix and A  −46 6  = 6  −46 6  Select the true statement/s o o A A13  −46 6  = (6)13  −46 6  B A7  −46 6  = 6...

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LINEAR ALGEBRA EXAM 4 version 1 name: 1. Suppose A is a square real matrix and A  −46 6  = 6  −46 6  Select the true statement/s o o A A13  −46 6  = (6)13  −46 6  B A7  −46 6  = 6  −46 6 7 C A7  −46 6  = (6)7  −46 6  D A6  −46 6  = (−7)13  −46 6  E A13  −46 6  = (−7)6  −46 6  F A6  −46 6  = (6)13  −46 6  G none of these 2. Suppose B is the set of COLUMNS of matrix M = −1 1 −10 6 8 0 0 0  and V be the space spanned by linear combi- nations ofB using real number scalars. Select true statement/s o o A  −30 5  is in spanned by columns of M B  −31 5  is spanned by columns of M C  −34 −1  is spanned by columns of M D  −34 −3  is not spanned by columns of M E rank(M) = 2 F  4−4 4  is spanned by columns of M G rank(M) = 4 H  10 0  IS spanned by columns of M I None of These 3. Suppose D =   12 1  ,  −20 0  ,  0−1 0  and B =  10 0  ,  01 0  ,  00 1  Suppose v⃗B =  02 −2  Determine the coordinates of this vector subject to basis D. o o A v⃗D =  −2−1 −6  B v⃗D =  −6−2 −11  C v⃗D =  02 −2  D None of These 4. Suppose B =   0−3 4  ,  −110 −1  and V be the space spanned by linear combinations of B using real number scalars. In other words V = α  0−3 4 + β  −110 −1  : α, β ∈ R  with the standard addition and the standard scalar multipli- cation. Select true statement/s o o A  05 −15  ∈ V B  0−2 1  ∈ V C  −641 16  ∈ V D  −859 20  ∈ V E  −892 −24  ∈ V F  −763 4  ∈ V G V is a vector space over R H None of These 5. ©2019 daabz.com LINEAR ALGEBRA EXAM 4 version 1 page 1 of ?? http://www.daabz.com/editQ.html?nID=2jF http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=1&key=4 http://www.daabz.com/editQ.html?nID=2ib http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=2&key=4 http://www.daabz.com/editQ.html?nID=2ir http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=3&key=4 http://www.daabz.com/editQ.html?nID=2ij http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=4&key=4 LINEAR ALGEBRA EXAM 4 version 1 (page 2/ ??) Suppose P and Q are a real 2 × 2 matrices. Suppose I is the 2x2 identity matrix, and Suppose PQ = I Select all necessarily true statements. o o A P +Q = 0 B (PQ)3 = P 3Q3 C P is invertible D (PQ)2 = PQ E P−1 does not exist F (PQ)2 = P 2Q2 G (don’t even try this if you have a small soul) QP = I H det(P ) > 0 I None of These 6. Suppose A is a square matrix, and det(A) ̸= 0 then A−1 is given by o o A A−1 = det(A) ·Adj(A) B A−1 = 1 det(A) Adj(A) C none of these 7. Suppose linear transformation T : R2 → R2 with T [ x y ] =[ 7x+ y 4x+ y ] Assume A is the matrix that represents the tran- formation T so that for ever vector v⃗ we have T (v⃗) = Av⃗ Select the true statement/s o o A T [ 0 1 ] = [ 1 1 ] B T [ 0 1 ] = [ −1 3 ] C A = [ 1 −1 0 3 ] D A = [ 1 1 −2 1 ] E T [ 1 0 ] = [ 1 0 ] F T [ 1 0 ] = [ 7 4 ] G A = [ 7 1 4 1 ] H None of These 8. Suppose A = [ 0 6 −1 −1 ] If it exists, find the inverse, A−1 o o A [ −16 −1 1 6 0 ] B inverse does not exist C [ 1 6 − 1 12 1 0 ] D [ 1 44 − 7 44 3 22 1 22 ] E none of these 9. Suppose V =   x1 x2 x3 x4  : x1 = x3 + x4, x2 = x3 − x4 . oo A A basis for V is   −1 0 1 1  ,  −1 1 0 2   B A basis for V is   1 1 1 0  ,  1 −1 0 1   C A basis for R4 is Basis(V ) ∪Basis(V ⊥) D V is a subspace of R4 E A basis for R4 is   1 1 1 0  ,  1 −1 0 1  ,  −1 0 1 1  ,  −1 1 0 2   F A basis for V ⊥ is   −1 0 1 1  ,  −1 1 0 2   G none of these ©2019 daabz.com LINEAR ALGEBRA EXAM 4 version 1 page 2 of ?? http://www.daabz.com/editQ.html?nID=2gt http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=5&key=4 http://www.daabz.com/editQ.html?nID=2hm http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=6&key=4 http://www.daabz.com/editQ.html?nID=2ja http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=7&key=4 http://www.daabz.com/editQ.html?nID=2fV http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=8&key=4 http://www.daabz.com/editQ.html?nID=2iI http://www.daabz.com/editQn.html?coursenid=1N&v=1&TaskType=exam&QuesNo=9&key=4