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Question 2 {(1,-,,,1)} and C {(1,-,0), 0, 0,1)} be subsets of R3 Let B (a) Show...
Question 2. Let B- (1,-1,1).(-1,1,1) and C(1,-1,0), (0,0, 1)) be subsets of R3 (a) Show that both the sets B and C are hnearly independent sets of vectors with spanB - 12 marks 2 marks spanC (b) Assu...
Question 2. Let B- (1,-1,1).(-1,1,1) and C(1,-1,0), (0,0, 1)) be subsets of R3 (a) Show that both the sets B and C are hnearly independent sets of vectors with spanB - 12 marks 2 marks spanC (b) Assuming the usual left to right ordering, find the transition matrix PB-C (c) Given a basıs D of R2, find the transition matrux Ps-D given 2 1 Pc.D 3 2 3 marks (d) Use the transition matrix Pc-.D in (c) to find D...
Can someone please help? Question 2. Let B = {(1,-1,1),(-1,1,1)} and C = {(1,-1,0),(0,0,1)} be subsets...
Can someone please help?
Question 2. Let B = {(1,-1,1),(-1,1,1)} and C = {(1,-1,0),(0,0,1)} be subsets of R3 (a) Show that both the sets B and C are linearly independent sets of vectors with span B = spanc (12 marks] (b) Assuming the usual left to right ordering, find the transition matrix PB- [2 marks] (c) Given a basis D of R?, find the transition matrix PB-D given Pc+b = (32) [3 marks (d) Use the transition matrix PC-D in...
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets...
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets which are subspaces, find a basis and the dimension for each of them
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace...
1 3. Consider the vector v= (-1) in R3. Let U = {w € R3 :w.v=0},...
1 3. Consider the vector v= (-1) in R3. Let U = {w € R3 :w.v=0}, where w.v is the dot product. 2 (a) Prove that U is a subspace of R3. (b) Find a basis for U and compute its dimension. 4. Decide whether or not the following subsets of vector spaces are linearly independent. If they are, prove it. If they aren't, write one as a linear combination of the others. (a) The subset {0 0 0 of...
5. (10pts) Let B (v1 (1,1,0), v2 (1,0,-1). v3 (0,1,-1)) be a basis of R3 Using...
5. (10pts) Let B (v1 (1,1,0), v2 (1,0,-1). v3 (0,1,-1)) be a basis of R3 Using the Gram-Schmidt process, find an orthogonal basis of R3. (You don't have to normalize the vectors.)
QUESTION 4 Let T R3-P2 be defined by T(a, b, c) - (a + b + e) +(a+b)a2 (4.1) Show that T is a linear transformation (4.2) Fınd the matrix representation [T]s, B, of T relative to the basıs in R3 and...
QUESTION 4 Let T R3-P2 be defined by T(a, b, c) - (a + b + e) +(a+b)a2 (4.1) Show that T is a linear transformation (4.2) Fınd the matrix representation [T]s, B, of T relative to the basıs in R3 and the basis in P2, ordered from left to right Determine the range R(T of T Is T onto? In other words, is it true that R(T)P2 Let x, y E R3 Show that x-y ker(T) f and only...
2. Let S-{a,b,c,d) and let F1, F2 be ơ-algebras of subsets of S2 given by a....
2. Let S-{a,b,c,d) and let F1, F2 be ơ-algebras of subsets of S2 given by a. Is FînF, a ơ-algebras of subsets of S2? Why (or why not)? b. Is F1 UF, a ơ-algebra of subsets of O? Why(or why not)? c. What is cardinality of 2 ( denoted by #(29) or 12 l). d. Find the Power set of (denoted by 2 ).
1 2 -1 0 0 1 0 0 -1 3 ſi 2 0 2 5 [10...
1 2 -1 0 0 1 0 0 -1 3 ſi 2 0 2 5 [10 (11 points) The matrix A= 2 1 3 2 7 reduces to R= 0 3 1 a 6 5 0 1 Let ui, , 13, 144, and us be the columns of U. (a) Determine, with justification, whether each of the following sets is linearly independent or linearly dependent. i. {u1, 12, 13) ii. {u1, 13, us} iii. {u2, 13} iv. {u1, 12, 13,...
detailed work pls axb. Find the angle Let a, b 0 be vectors in R3 with...
detailed work pls axb. Find the angle Let a, b 0 be vectors in R3 with angle between them #/7, and e 3. between each pair of vectors: c and b c and b x a b and b x c a and b x c axcand b xc
detailed work pls axb. Find the angle Let a, b 0 be vectors in R3 with angle between them #/7, and e 3. between each pair of vectors: c and b...
Let A, B, C be subsets of U. Prove that If C – B=0 then AN...
Let A, B, C be subsets of U. Prove that If C – B=0 then AN (BUC) < ((A-C)) UB
Question 2. Let B- (1,-1,1).(-1,1,1) and C(1,-1,0), (0,0, 1)) be subsets of R3 (a) Show that both the sets B and C are hnearly independent sets of vectors with spanB - 12 marks 2 marks spanC (b) Assuming the usual left to right ordering, find the transition matrix PB-C (c) Given a basıs D of R2, find the transition matrux Ps-D given 2 1 Pc.D 3 2 3 marks (d) Use the transition matrix Pc-.D in (c) to find D...
Can someone please help?
Question 2. Let B = {(1,-1,1),(-1,1,1)} and C = {(1,-1,0),(0,0,1)} be subsets of R3 (a) Show that both the sets B and C are linearly independent sets of vectors with span B = spanc (12 marks] (b) Assuming the usual left to right ordering, find the transition matrix PB- [2 marks] (c) Given a basis D of R?, find the transition matrix PB-D given Pc+b = (32) [3 marks (d) Use the transition matrix PC-D in...
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets which are subspaces, find a basis and the dimension for each of them
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace...
1 3. Consider the vector v= (-1) in R3. Let U = {w € R3 :w.v=0}, where w.v is the dot product. 2 (a) Prove that U is a subspace of R3. (b) Find a basis for U and compute its dimension. 4. Decide whether or not the following subsets of vector spaces are linearly independent. If they are, prove it. If they aren't, write one as a linear combination of the others. (a) The subset {0 0 0 of...
5. (10pts) Let B (v1 (1,1,0), v2 (1,0,-1). v3 (0,1,-1)) be a basis of R3 Using the Gram-Schmidt process, find an orthogonal basis of R3. (You don't have to normalize the vectors.)
QUESTION 4 Let T R3-P2 be defined by T(a, b, c) - (a + b + e) +(a+b)a2 (4.1) Show that T is a linear transformation (4.2) Fınd the matrix representation [T]s, B, of T relative to the basıs in R3 and the basis in P2, ordered from left to right Determine the range R(T of T Is T onto? In other words, is it true that R(T)P2 Let x, y E R3 Show that x-y ker(T) f and only...
2. Let S-{a,b,c,d) and let F1, F2 be ơ-algebras of subsets of S2 given by a. Is FînF, a ơ-algebras of subsets of S2? Why (or why not)? b. Is F1 UF, a ơ-algebra of subsets of O? Why(or why not)? c. What is cardinality of 2 ( denoted by #(29) or 12 l). d. Find the Power set of (denoted by 2 ).
1 2 -1 0 0 1 0 0 -1 3 ſi 2 0 2 5 [10 (11 points) The matrix A= 2 1 3 2 7 reduces to R= 0 3 1 a 6 5 0 1 Let ui, , 13, 144, and us be the columns of U. (a) Determine, with justification, whether each of the following sets is linearly independent or linearly dependent. i. {u1, 12, 13) ii. {u1, 13, us} iii. {u2, 13} iv. {u1, 12, 13,...
detailed work pls axb. Find the angle Let a, b 0 be vectors in R3 with angle between them #/7, and e 3. between each pair of vectors: c and b c and b x a b and b x c a and b x c axcand b xc
detailed work pls axb. Find the angle Let a, b 0 be vectors in R3 with angle between them #/7, and e 3. between each pair of vectors: c and b...
Let A, B, C be subsets of U. Prove that If C – B=0 then AN (BUC) < ((A-C)) UB
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