Homework Answers
o 1 0 -1 Exercise 2. Let A= in M3,R, and ✓ = 0 in R3....
o 1 0 -1 Exercise 2. Let A= in M3,R, and ✓ = 0 in R3. -1 0 For every vector W E R3, set g(W) = WT AT ER. (i) Show that g: R3 → R defines a linear transformation. What is the matrix [g]C,B in the - 1 bases C = {1} and B { 8.00 } ? (ii) Let f : R3 → R be the function defined by f() = 7T Aw E R. Show that...
1 1 1 0 1 Let A 0 0 and B 1 0 1 0 1...
1 1 1 0 1 Let A 0 0 and B 1 0 1 0 1 0 0 1 0 1 1. If C = A o B, then C31 0 and C21 1 2. If E = AV B, then E32 1 3. If G = A AB', then G 12 = 1
linear algebra Problems 1. Let A= 3 3 0 5 2 2 0 -2 4 1...
linear algebra
Problems 1. Let A= 3 3 0 5 2 2 0 -2 4 1 -3 0 2 10 3 2 (a) Identify the (1,4)-minor A14 (b) Find the (3,2)-cofactor C32.
Let B = {(1,0), (0, 1)} and B' = {(0, 1), (1, 1)} be two bases...
Let B = {(1,0), (0, 1)} and B' = {(0, 1), (1, 1)} be two bases for the vector space V = RP. Moreover, let [y]g = [1 -2]" and the matrix for T relative to B be 2 A= 22 -2 2. (a) Find the transition matrix P from B' to B. (b) Use the matrices P and A to find [v] and [T(0) В" (C) Find A' (the matrix for T relative to B'). (d) Find (T(m)]g
Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E ] 5. V i 6. V i 7. E ( E) 8. E Construct the LR(0...
Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E ] 5. V i 6. V i 7. E ( E) 8. E Construct the LR(0) DFA for this grammar a) b) Construct the LR(0) parsing table. Is it LR(o)? Why and why not?
Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E...
1 1 0 -1 Exercise 2. Let A = 0 1 0 in M3,R, and ✓...
1 1 0 -1 Exercise 2. Let A = 0 1 0 in M3,R, and ✓ = 0 in R3. -1 0 For every vector W E R”, set g(ū) = WT AV E R. (i) Show that g: R3 → R defines a linear transformation. What is the matrix [g]c,b in the bases C = {1} and B = { 9 8 B |}? (ii) Let f: R3 + R be the function defined by f(w) = vſ Aw...
O 2 1 1 02 O -2 102 5. Let A 0 -2 0 B 0...
O 2 1 1 02 O -2 102 5. Let A 0 -2 0 B 0 and C O 1 0 4 1. 1 0 4 -1 0 4 (a) Find an elementary row operation that transforms A into B. O 2 (b) Find an elementary row operation that transforms B into C. (c) By means of several additional operations, transform C into I3 (d) What is the rank of the matrix A? Explain.
Question 11 (1 point) Use following diagram to answer the question . o Let B represents...
Question 11 (1 point) Use following diagram to answer the question . o Let B represents the event that right die shows an even number. Find P(B)? 1/2 1/3 1/4 o e oo hp . 000 a . Let B represents the event that right die shows an even number. Find P(B)? 0 1/2 0 1/3 1/4 2/3 1 o W g 1 e Oo
2. Let U C R2 be simply connected and let to E U. Let g: U(oR2 be irrotational and of class C1. A...
2. Let U C R2 be simply connected and let to E U. Let g: U(oR2 be irrotational and of class C1. Assume that there exists r >0 such that B(zo, r) C U and g=0. Let γ be a closed sinile polygonal arc with range in U \ {zo), let「be its range, and let V be the bounded connected component of R2 \ Г. (a) Assume that V C U \ [xo) and prove that g=0. (b) Assume that...
HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6...
HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6 -2 1 a. (4 pts) Find the multipliers l21, 131,132 and the elemention matrices E21, E31, E32 b. (2 pts) Use the multipliers l21, 131,132 to construct the lower triangular matrix, L c. (2 pts) Use the elimination matrices to determine the upper triangular, U, matrix of A d. (2 pts) verify that LU A
o 1 0 -1 Exercise 2. Let A= in M3,R, and ✓ = 0 in R3. -1 0 For every vector W E R3, set g(W) = WT AT ER. (i) Show that g: R3 → R defines a linear transformation. What is the matrix [g]C,B in the - 1 bases C = {1} and B { 8.00 } ? (ii) Let f : R3 → R be the function defined by f() = 7T Aw E R. Show that...
1 1 1 0 1 Let A 0 0 and B 1 0 1 0 1 0 0 1 0 1 1. If C = A o B, then C31 0 and C21 1 2. If E = AV B, then E32 1 3. If G = A AB', then G 12 = 1
linear algebra
Problems 1. Let A= 3 3 0 5 2 2 0 -2 4 1 -3 0 2 10 3 2 (a) Identify the (1,4)-minor A14 (b) Find the (3,2)-cofactor C32.
Let B = {(1,0), (0, 1)} and B' = {(0, 1), (1, 1)} be two bases for the vector space V = RP. Moreover, let [y]g = [1 -2]" and the matrix for T relative to B be 2 A= 22 -2 2. (a) Find the transition matrix P from B' to B. (b) Use the matrices P and A to find [v] and [T(0) В" (C) Find A' (the matrix for T relative to B'). (d) Find (T(m)]g
Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E ] 5. V i 6. V i 7. E ( E) 8. E Construct the LR(0) DFA for this grammar a) b) Construct the LR(0) parsing table. Is it LR(o)? Why and why not?
Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E...
1 1 0 -1 Exercise 2. Let A = 0 1 0 in M3,R, and ✓ = 0 in R3. -1 0 For every vector W E R”, set g(ū) = WT AV E R. (i) Show that g: R3 → R defines a linear transformation. What is the matrix [g]c,b in the bases C = {1} and B = { 9 8 B |}? (ii) Let f: R3 + R be the function defined by f(w) = vſ Aw...
O 2 1 1 02 O -2 102 5. Let A 0 -2 0 B 0 and C O 1 0 4 1. 1 0 4 -1 0 4 (a) Find an elementary row operation that transforms A into B. O 2 (b) Find an elementary row operation that transforms B into C. (c) By means of several additional operations, transform C into I3 (d) What is the rank of the matrix A? Explain.
Question 11 (1 point) Use following diagram to answer the question . o Let B represents the event that right die shows an even number. Find P(B)? 1/2 1/3 1/4 o e oo hp . 000 a . Let B represents the event that right die shows an even number. Find P(B)? 0 1/2 0 1/3 1/4 2/3 1 o W g 1 e Oo
2. Let U C R2 be simply connected and let to E U. Let g: U(oR2 be irrotational and of class C1. Assume that there exists r >0 such that B(zo, r) C U and g=0. Let γ be a closed sinile polygonal arc with range in U \ {zo), let「be its range, and let V be the bounded connected component of R2 \ Г. (a) Assume that V C U \ [xo) and prove that g=0. (b) Assume that...
HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6 -2 1 a. (4 pts) Find the multipliers l21, 131,132 and the elemention matrices E21, E31, E32 b. (2 pts) Use the multipliers l21, 131,132 to construct the lower triangular matrix, L c. (2 pts) Use the elimination matrices to determine the upper triangular, U, matrix of A d. (2 pts) verify that LU A
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