2 Suppose A = is positive semi definite matrix then: 10 O a. a < -V20 O b. a = ±v20 O c. lal < 20 O d. lal < v20

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: 2. Regarding DFT matrix W₁, prove that W 1 = W for N=4. N

A: Consider the given equation, WN-1=1NWNH for N=4 Where, WN is a DFT matrix. So, as we know that,…

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: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: Q4 For the following three matrices : k A= 0.5 2k 0.5 12 8 2kl [22 16 C=11 8 4 k 1 3 B= m 2 11 ml…

A: Given

Q: At Compute the matrix exponential e for the system x' = Ax given below. x₁ = 37x₁ - 36x₂, x 2 = 34x₁…

A:

Q: For which value of x is the following matrix not invertible: 1 1 3x A = 3x 3x 3x 3x 3x O 2 4 O1/3 1

A:

Q: Suppose T: R° → Rª is defined by T(x) Mx and M is a 24 x 19 matrix. Then %3D a = b =

A: If T: from Rb to Ra then M is always a×b matrix.

Q: Suppose A = 2 a) is positive semi definite matrix then: a 10 O a Ja < 20 O b. a <-V20 O. lal < v20 O…

A: A positive semi definite matrix is the one whose eigen values are greater than or equal to zero. So,…

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: 2. (a) Suppose (B − C)D = 0, where B and C are m x n matrices and D is invertible. Show that B = C.…

A: Explanation of the answer is as follows

Q: r every square matrix A = (a;;) € Μπ(C) η |4||, = sup ||Ax|t Σ = max Elai TEC ||z||1=1 π Alloo sup…

A:

Q: Let A(t) be a n × n matrix whose coefficients are continuous functions of t on the interval (α, β).…

A:

Q: Set up the 4 x 3 matrix E with E¡i = 0; = Vdi (the ith singular value) and all other Eij = 0.

A:

Q: Suppose that T() and 7 () -E Find the standard matrix A for Tand find T(:) 14 and 2 and T (HD A-3…

A:

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: ve that for every matrix A, (AT)T = A

A: We have to prove that transpose of A transpose is A.

Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. If B is a singular matrix then…

A: We have given  det(A) = 3 If B is singular matrix  det(B)  = 0 detBT=det(B) =0 So,  det2A-2BT =0…

Q: (4) Given matrix A = and that h(T) = T² – 2T – 7, find h(T).

A: We use properties of matrix

Q: If Q+A= A holds for every m×n matrix A, show that Q = 0mn.

A: Consider the given equation, Q=A+A   Now, subtract the matrix A from both side: Q+A-A = A -A As, A…

Q: 11. Let A be an m x n matrix and let x, y e R". Prove that if Ax = 0 and y = ATb for some b e R",…

A:

Q: Suppose that the system x' = Ax + g(x) is locally linear near the O as x → 0, and that A is a 2 x 2…

A:

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: Given X, = [-1,0]'.do [-1,1]", go = [2,0] and G(X,)s 2. Then f(X) - f(X1) 2 ((G(X,) means the…

A: As per the question we are given : X0 = [-1  0]T , d0 = [-1  1]T , g0 = [2  0]T , ||G(X1)|| ≤ 2 And…

Q: (i) Use the properties of trace to argue that tr(AʼA) = tr(AA') for any n × m matrix A. [2 0 (ii)…

A:

Q: Let A be a square invertible matrix. Which of the following is not true? Select one alternative: O A…

A: Since given A is invertible matrix, so det(A) is not equal to zero. It is always true. we also know…

Q: Consider the systenm X' = AX. where A is 2×2 matrix. If D(x) =| (1+2r)e for given system. Then the…

A:

Q: (d) Suppose A is a 2 × 2 matrix such that for all x, y E R?, (Ax) · (Ay) = x · y Must it be true…

A: This is the problem of linear transformation.

Q: Verify by finding the matrix of S 0 T (a) by direct substitution and (b) by matrix multiplication of…

A:

Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. If B is a singular matrix then…

A: Let A and B be two matrices of size 4 x 4

Q: Compute the matrix exponential e At for the system x' = Ax given below. x²₁ = 20x₁ − 20x₂, x′2 =…

A:

Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. %3D If B is a singular matrix then…

A:

Q: (4) Given matrix A = G ). and that h(T) = T² – 2T – 7, find h(T).

A:

Q: The Hessian matrix for f(x) = x³x3 + x2x3 at the point [1 2 3] is given by: [6 0 31 [18 0 31 [3 0 6]…

A:

Q: Suppose that A is an n x n matrix and det(A) = 2, det(A +I) = 3, and det(A+2I) = 5. Compute the…

A:

Q: For which valua of k does the matrix 1 have real eigrenvalue of one multiplic ety 2 a to

A:

Q: Is the following matrix a Hermitian or Skew-He rmitian, and find the 2 3 – 2i 1+i A X = -3 – 2i 2…

A:

Q: 16 - х For what value of x, 13. 47 is a singular matrix: - A. 1 В. 2 С. -1 D. -2 E. None of the…

A: A matrix A is said to be singular if its determinant is zero .

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: The matrix is defined as A= 1 has characteristic equation of 22 + DA + 3, so the value of D…

A:

Q: Consider M as an n x n matrix, we can say that M is nilpotent  if Mx = 0 for some x ∈ +Z . Now:…

A: (a) Let M be a nilpotent matrix .  So, using definition of nilpotent, Mx=0 for some x∈ℤ+ ⇒Mx=0⇒Mx=0…

Q: Consider matrix K of order 3 defined by 3sene 3cose K = -3cose 3sene \3sene - 3cose 3sene + 3cose 3,…

A: To find the cofactor of the matrix

Q: Q4/ For the following three matrices : k k 1 3. B= m 4 [22 16] A= |0.5 2k 0.5 2 C= |11 8. 8 2k. .1…

A:

Q: (4) Given matrix A= and that h(T) = T – 2T – 7, find h(T).

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…