Can someone help me with this question please?
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Can someone help me with this question please?
5. (3 pts) State whether the following statements...
please provide detailed explanation with answer 3-10. True or False: (a) If u and v are...
please provide detailed explanation with answer
3-10. True or False: (a) If u and v are column vectors in R", then u. v = utv. (b) If A is a square matrix satisfying A2 = 0, then A = 0. (c) If A is a square matrix satisfying A2 = A, then A = EI or A = 0. (d) There is a square matrix A (of any dimension) such that A2 = -1. (e) If A and B are...
Decide whether each statement is true or false and explain your reasoning. Give a counter-example...
Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...
1. True or False. Decide whether the following statements are true or false. Circle your answer...
1. True or False. Decide whether the following statements are true or false. Circle your answer (no explanation needed). (a) (3 points) If ū1, víz, vz, ū are vectors for R“, and {vi, uz, uz} is lincarly independent, then {61, U2, U3, } is also lincarly independent. True False (b) (3 points) If ū is a vector in R™ and W is a subspace of R", and ū= projw (ū) is the closest point on W to ū, then i...
Can someone please explain how to solve the problem below? 6. State Space Systems: a. (5...
Can someone please explain how to solve the problem below?
6. State Space Systems: a. (5 pts) Determine the state space system in controllable canonical form that implements the transfer function Y(s)_ 252 +5 U(s) s+4s+7s +12 b. (10 pts) For the state space system given below, design a controller u =-Kx+v such that the eigenvalues of the closed loop system are -10, – 20. To 17 , y = Cx C = [25] x = Ax+Bu with A= ln...
Determine, with justification, whether each of the following statements is true or false. (a) IfV is...
Determine, with justification, whether each of the following statements is true or false. (a) IfV is a vector space and S, and S2 are two bases of V, then Si U S2 is a basis of V. (b) Let A and B ne matrices of the same size. If A and B have the same row space, then they have the same column space. (c) Let M be an n x n square matrix. If M has less than n...
For the following six questions, indicate whether the following statements are true or false. In each...
For the following six questions, indicate whether the following statements are true or false. In each case give a reason for your answer. Problem 13 [10 pts) If L:V +W is a linear transformation of vector spaces and U CW is a subspace of W, then {v € V | L(v € U} CW is a subspace of V. Problem 14 (10 pts) The set {A E R2x2 | A is nonsingular} is a subspace of R2x2. Problem 15 (10...
(1 point) Are the following statements true or false? ? 1. u? v – vſ u...
(1 point) Are the following statements true or false? ? 1. u? v – vſ u = 0. ? 2. If x is orthogonal to every vector in a subspace W , then x is in Wt. ? 3. For any scalar c, ||cv|| = c||v. ? 4. For an m x n matrix A, vectors in the null space of A are orthogonal to vectors in the row space of A. ? 5. If u and v are nonzero...
Question 4 2 pts Determine whether the vector u is in the column space of the...
Question 4 2 pts Determine whether the vector u is in the column space of the matrix A and whether it is the null space of A. 1 0 3 1 -2 1 - 4 U = 3 3 0 4 - 1 3 6 Not in Col A in Nul A In Col A, not in Nul A Not in ColA, not in Nul A In Col A and in Nul A Question 5 1 pts 1 co 2...
Please Do it clearly and ASAP UNIC HaHdheld ull, 130 points is a "perfect" score. Good luck! Part I. True False. Circle T if the statement is always true, and F if the statement is at leas...
Please Do it clearly and ASAP
UNIC HaHdheld ull, 130 points is a "perfect" score. Good luck! Part I. True False. Circle T if the statement is always true, and F if the statement is at least sometimes false. [10 pts] 1) T F RREF(A) is unique. 2) T F The solution set to "Ax b" is a vector space. 3) T F Every square matrix is diagonalizable. 4) T F Adding a column to a column of annxn A...
(1 point) Are the following statements true or false? ? 1. If z is orthogonal to...
(1 point) Are the following statements true or false? ? 1. If z is orthogonal to uị and u2 span(uj, u2), then z must be in and if W = Wt. ? 2. For each y and each subspace W, the vector y – projw(y) is orthogonal to W. ? 3. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. ? 4. The orthogonal projection p of y onto a subspace...
please provide detailed explanation with answer
3-10. True or False: (a) If u and v are column vectors in R", then u. v = utv. (b) If A is a square matrix satisfying A2 = 0, then A = 0. (c) If A is a square matrix satisfying A2 = A, then A = EI or A = 0. (d) There is a square matrix A (of any dimension) such that A2 = -1. (e) If A and B are...
Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...
1. True or False. Decide whether the following statements are true or false. Circle your answer (no explanation needed). (a) (3 points) If ū1, víz, vz, ū are vectors for R“, and {vi, uz, uz} is lincarly independent, then {61, U2, U3, } is also lincarly independent. True False (b) (3 points) If ū is a vector in R™ and W is a subspace of R", and ū= projw (ū) is the closest point on W to ū, then i...
Can someone please explain how to solve the problem below?
6. State Space Systems: a. (5 pts) Determine the state space system in controllable canonical form that implements the transfer function Y(s)_ 252 +5 U(s) s+4s+7s +12 b. (10 pts) For the state space system given below, design a controller u =-Kx+v such that the eigenvalues of the closed loop system are -10, – 20. To 17 , y = Cx C = [25] x = Ax+Bu with A= ln...
Determine, with justification, whether each of the following statements is true or false. (a) IfV is a vector space and S, and S2 are two bases of V, then Si U S2 is a basis of V. (b) Let A and B ne matrices of the same size. If A and B have the same row space, then they have the same column space. (c) Let M be an n x n square matrix. If M has less than n...
For the following six questions, indicate whether the following statements are true or false. In each case give a reason for your answer. Problem 13 [10 pts) If L:V +W is a linear transformation of vector spaces and U CW is a subspace of W, then {v € V | L(v € U} CW is a subspace of V. Problem 14 (10 pts) The set {A E R2x2 | A is nonsingular} is a subspace of R2x2. Problem 15 (10...
(1 point) Are the following statements true or false? ? 1. u? v – vſ u = 0. ? 2. If x is orthogonal to every vector in a subspace W , then x is in Wt. ? 3. For any scalar c, ||cv|| = c||v. ? 4. For an m x n matrix A, vectors in the null space of A are orthogonal to vectors in the row space of A. ? 5. If u and v are nonzero...
Question 4 2 pts Determine whether the vector u is in the column space of the matrix A and whether it is the null space of A. 1 0 3 1 -2 1 - 4 U = 3 3 0 4 - 1 3 6 Not in Col A in Nul A In Col A, not in Nul A Not in ColA, not in Nul A In Col A and in Nul A Question 5 1 pts 1 co 2...
Please Do it clearly and ASAP
UNIC HaHdheld ull, 130 points is a "perfect" score. Good luck! Part I. True False. Circle T if the statement is always true, and F if the statement is at least sometimes false. [10 pts] 1) T F RREF(A) is unique. 2) T F The solution set to "Ax b" is a vector space. 3) T F Every square matrix is diagonalizable. 4) T F Adding a column to a column of annxn A...
(1 point) Are the following statements true or false? ? 1. If z is orthogonal to uị and u2 span(uj, u2), then z must be in and if W = Wt. ? 2. For each y and each subspace W, the vector y – projw(y) is orthogonal to W. ? 3. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. ? 4. The orthogonal projection p of y onto a subspace...
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