5. Compute the condition number K(A) of the following matrix 1 1+€ 1 1 1 A 1 1 1 1+€ What is k(A) as ɛ → 0?

Q: 2 Suppose A = is positive semi definite matrix then: a 10 O a. Jal < 20 O b. a <-v20 Oc lal < v20 O…

A: Suppose A=2αα10 is a positive semidefinite matrix then which of the following is correct.

Q: |8 3 | 2 7 al, where a is tity matrix, its %D

A:

Q: [2.25] Show that C= {x : Ax <0}, where A is an m × n matrix, has at most one extreme point, the…

A: 2.25)   show that C=x:Ax≤0 where A is an m×n matrix , has at most one extreme point, the origin.…

Q: 1 Suppose that a 3 x 3 matrix A has det A = 1 and that its cofactor matrix is C = 1 2 |-7 4 2 Find…

A: Formula: Let A be a n×n matrix with non zero determinant then, A-1=1det ACT where C is the cofactor…

Q: D If A = K [-P M 2P S 3 is a singular matrix then find the value of P.

A: Given matrix is A=DM2PK3S-PRL. Consider D=1, L=9, P=f, S=1, N=8, K=9, M=3 and R=5. Then the given…

Q: Compute the rank and nullity of the given matrices over the indicated Zp

A:

Q: 2 1 Which of the following is the matrix C that satisfies the equality (CT- 412) 5 3 -1 (a) -5 (b) 1…

A:

Q: .

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Q: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

Q: 9. Suppose that M is a 2 × 2 matrix over R, with characteristic polynomial det(AI – M) = X² – 21 + 3…

A:

Q: 2 1 -1 4 previous problem to determine a matrix S such that Show that A is defective and use the 3…

A:

Q: 1 0 0 0 1 0 9. Suppose M Which matrix is M1? %3D 0 3 1 1 00 1 3 0 0 1 0. -3 0. 0. 1 O (1 0 0 0 1 0.…

A: Finding inverse of M

Q: Jump to level 1 E) 4x1 – x2 Let T : R° → R² be defined by T X2 2x3 x3 4 Let B = uj = 1 u2 -2 and C…

A: Consider the provided information, Tx1x2x3=4x1-x22x3 And the basis B=u1=-114,u2=-66-3,u3=5-2-4 and…

Q: **15. Suppose A is an m × n matrix and x e R" satisfies (AA)x = 0. Prove that Ax = 0. (Hint: What is…

A:

Q: in number 1, B is the matrix representation of Z with respect to B only, not B and B'. The formula…

A:

Q: 12 6 . Determine the rank and nullity of the matrix C=|0 1

A:

Q: 5. Let T be defined as in problem 4. Let B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}. Find the matrix…

A: See the detailed solution below.

Q: 1. Find a condition on a, b, c, d such that the augmented matrix " E b has a unique solution.

A: The condition on a,b,c,d must be a relation between a,b,c,d.

Q: One of the following is not an elementary matrix 100 100 a) 0 0 1 b) 0-50 020 0 0 1 104 00 1 010 d)…

A:

Q: .1 Suppose A is a matrix with characteristic polynomial CA(x) = x²(x – 1)³(x+2)². Determine the…

A: The solution are next step

Q: 2 4 8 Suppose that A = LDU = 039 , then the matrix U is 0 0 7 equal to: 2 00 0 3 0 0 0 7 1 2 4 0 1 3…

A: Given:Suppose A=LDU=248039007To find : Matrix U

Q: Consider the following inputs coefficient matrix: 0.25 0.4 0.2 A = 0.25 0.1 0.1 0.25 0.1 0.3 Find…

A: Remark: The minor of an element in a matrix is the value of the determinant of the matrix that…

Q: 1. Given the input-coefficient matrix for a hypothetical [0.1 0.51 0.3 0.2 economy made up of only…

A: Given that,

Q: 4. Suppose A is a nonsingular matrix with SVD A= UEV*.

A:

Q: **32. Suppose A is an m x n matrix and x e R" satisfies (ATA)x = 0. Prove that Ax = 0. (Hint: What…

A: Here we use property of modular and dot product.

Q: Suppose that A is an n x n matrix. Prove that nulity(a)=nullity(AT)

A:

Q: 7. The rank of an identity matrix of order n is: А. п - 1 В. п C. n+1 D. 0

A:

Q: A matrix B in Mnxn (C) is called skew-symmetric if Bt= -B. Prove that if B ϵ Mnxn (C) is…

A: Let B be skew-symmetric matrix of order n, where n is odd, then we have

Q: The consumption matrix C for the U.S economy in 1972 has the property that every entry in the matrix…

A: Given

Q: §8.3, Exercise 5. Suppose the mapping L : R³ → R² is linear and satisfies (:)-(3) ()-6) ()- ) 1 1 2…

A:

Q: 1 4 What is a, if A = is a singular matrix ? %3D 2 a

A:

Q: 3. Find that whether the following matrix is singular or nonsingular. 8- 01 0 - 0 -5] 0 - O 0

A: Singular and Non-singular matrix- Let A be a square matrix, such that the determinant of A is…

Q: : Show that there are no nxn matrices A and B such that AB – BA= In. & You may cite, without…

A:

Q: 3. Show that for any n x n matrix A of rank r, we have ||4|| < ||4||ES VFl|4||.

A: To show that: A≤AF≤ rA  for any n×n matrix A of rank r.

Q: 2. Consider the 6 x 8 matrix [1 30 0 0 0 10 -3 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 5 6. 4. 0 -7 8 -9 A…

A: The dimension of ColA is the number of pivot columms in the corresponding echelon form of A. If A is…

Q: Suppose that A is an n × n matrix and det A + 0. Determine the rank and nullity of A.

A:

Q: Compute the matrix exponential e^At for the system x′=Ax given below.   x′1=11x1−10x2​, x′2=8x1−7x2…

A:

Q: 1) Suppose that T is a linear operator with standard matrix 8 3 6 0 2 0 0 7 Is T one-to-one?…

A: Given the linear operator T:ℝ3→ℝ3 836025007 Now, we find determent of T.…

Q: 7. If a n x n matrix B is obtained from A, using only m number of row interchanges, then det A det B…

A:

Q: 1. Suppose (B – C) D = 0, where B and C are m x n matrix and D is invertible. Show B = C

A: ( B - C )D = 0 where B and C are m × n matrix and D is invertible.  Then, we have to prove that B =…

Q: 4. Suppose that xa is an approximate solution to the system of Ax = b. Let A, and Tare nonsingular…

A: Sol

Q: Let A = 0 1] 3 03 0 0 2 = If possible, construct P and D such that A don't need to compute P-¹).…

A:

Q: 13. Suppose that a 3 × 3 matrix A factors into a product 1 0 1 Determine the value of det(A).

A: It is known that for n×n matrices A and B detAB=detAdetB                      (i) Given…

Q: 3.1.Let a matrix B is B = FindB6 by using anonsingularmatrix P suchthatD = P¯-"BP is diagonal.

A: We are given: B = 2213 We need to find out B6 using P-1BP. This can be done as follows:

Q: One of the following is not an elementary matrix 100 100 a) 00 1 b) 0 -5 0 020 0 0 1 104 001 c) 010…

A:

Q: 4. Suppose that a, b, c, d, x, y, z are real numbers, and consider the matrix 0 0 0 d 0 0 c 0 b y 0…

A:

Q: [*:* а + 2 а (10) Find all a E R for which the matrix is singular. 1 а

A: Remark: A square matrix A of n is said to be singular if and only if det(A) = 0. i.e., Its…