Suppose C(A) = C(A") where A is m x n matrix, then %3D O a. r=m O b. m=n C. mn

Q: Give the matrix X such that -1 -1 3. -2 X = 0. -5 Type DNE 4. -5 1 0. 0. if such a matrix does not…

A: Given: 02-135-2-3-51X=-1000-50004 If AX=B, then X= A-1B. We know that A-1=adjAA and adjA= cofaijT

Q: 2. For the matrix 2 2 -1 B -3 3 find its Pseduoinverse Bt and the 2-norm ||B*||2.

A: Given : B=212-1-1-3-13 To find : pseudoinverse B+ and the 2-norm ∥B+∥2

Q: Suppose C is the cofactor matrix of matrix A and A CT then O a JA| = 0.5 %3D Ob.A= 1 %3D Od. A=+1

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Q: #12. Let A be an m × n matrix and B be an n × p matrix. Prove that (a) N(B) C N(AB). (b) C(AB) C…

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Q: 2. (a) Let S= A 0 I B A, B & GL (R), B = B, A = (B n ¸ Check whether or not S SP2n(R). Also give an…

A: Here , I use latex to write the answer.

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Q: ^ - [ 3 ] and B = [² = 4 5 If A 4 5 7 6 find 3A-2B+ I where I is a unit matrix.

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Q: .

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Q: 5.PT. PLN has $140000 to invest. The alternative investments and the corresponding annual returns…

A: According tot he given information it is required to form an linear programming problem for the…

Q: If A = [1 2 3], which type of the given matrix A ?

A: Given Matrix A=[1  2  3 ]1×3  Here number of row=1  Number of columns=3

Q: Let A = 1.8 -6 : J.c = , ].- [1 2 l4 5 6] [1 0 lo 1 [0] ol.C = 6 , and V = |1|. What is the sum of…

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Q: • Let f(u) = a'u = Li=1 a;Ui for a, u E R“. Calculate Vuf(u).

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: 8. Prove that (i) ||7. =1, and (ii) |. =\n (I is the Identity Matrix of order n).

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Q: Let A and B two matrices of order n x n. Prove the follwoing claims: (a) N(A)NN(B) CN(A+ B). (b)…

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Q: O Consider a non-singular n x n matrix A. Let A = inf{||SA|| : A+ 8A is singular}. Show that 1 A…

A: We are given a non-singular n×n matrix A and ∆ = inf{||δA|| : A+δA is singular} And we have to show…

Q: . Prove that (i) . =1, and (ii) ||, =\n (I is the Identity Matrix of order n).

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Q: Let A be an m x n matrix. Show that: ( a ) Ifxε Ν (Α'Α), then AxE R(Α) Ω Ν (A"). (b) N (AT A) =…

A: Let A be an  m×n matrix. Show that: (a) If x∈NATA, then Ax∈RA∩NAT (b) NATA=NA. (c) A and AT have…

Q: 1 2 Compute the adjoint matrix of A 3 2 2 2 3 Select one: a. -7 4 -5 7 -7 -5 3 -1 -2 %3D -7 -5 41 d.…

A: We have given a matrix and we have to find the adjoint of A.

Q: Assume B is an n × n matrix, n > 1, and det(B) = 4. (a) Find n such that det(−5B) = 100

A: Given:We are required to find:

Q: 15. If A=| B = 0 1 and C = |1 0 then find the matrix (Av B) 0 c

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Q: 10. Given that A and B are square matrices of order 3. If |A| = 3 and |B|= 1 then A. 2A 4B| = (-4)23…

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Q: Show that if n > 2 and C is an n x n matrix with cij = i + j, then det C = 0.

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Q: Let A be a 3x6 matrix of rank 3 then nullity of A equal 0 Select one: O True O False

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: If the matrix A is m x n and A = b is solvable for every b then O a. C(A) = Rm O b. m > n O c. C (A)…

A: For first question: Option (a) is correct. C(A) = R^m.

Q: Let f(u) = u™ Au, where u e Rd and A e Rd×d is a symmetric matrix. Calculate Vuf(u).

A: Directional derivative: If the function f is differentiable at x, then the directional derivative…

Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

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Q: A is a reversible matrix of nXn. Show that |adjA|=|A|r1

A: As we know that the inverse of a matrix A is : A-1=adj(A)|A|