Suppose Q(x) = x" Ax %D for some symmetric matrix А, and that we have a diagonal matrix D and a non-orthogonal matrix P such that D = P¯'AP. Then the smallest diagonal entry of D is the minimum value of Q(x) on ||x|| = 1. %3D True False

Q: The ODE (x dy/dx = yx²) is separable. true false If for a square matrix A and B, null matrix O, AB =…

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Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

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Q: 7. A type of bacterium doubles cach hour. a) If there are 4 bacteria in a sample, write a…

A: Since there are multiple questions the first question is answered.Kindly re post the question with…

Q: Verify that if r < s, then rows rand s of a matrix can be interchanged by performing 2(s - r) - 1…

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Q: the given matrix B, =[3 B Show that the matrix B is diagonalizable [Cite any theorems used] Find…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 1.) Let A = Obtain a matrix that is similar to A.

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Q: Let A € Rmxn, B € Rmxp be any matrix. Solve the following problem _min_ ||AX – B||2/17. XERnxp Hint:…

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Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: 2) An n x n matrix A is called nilpotent if Ak = 0 for some positive integer k. Show that if A + 0…

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Q: Let C be a 5 x 7 matrix with a rank 4. (1) What is the dimension of the solution space of Ax 0?

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Q: Let A be a matrix that satisfies ?^2 =? where ? is the identity matrix. a. Find a 2x2 example of…

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Q: Let -3 4 A-[ 3³ -1], E-[42], F-[^2} = = = -5 Compute the indicated matrix. (If this is not possible,…

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Q: Suppose 6 x 9 matrix A is rank 5. What is the nullity of A?

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Q: (1) Let A be a px5 matrix, B be amx 4 matrix. If AB is a 7xq matrix, then p= , m=_

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Q: 8. For the column matrix v=(v₁) we have explain then: (VA); =Vkaki

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Q: Show that the matrices [1 1 1] A = |1 3 0 and B = |0 o 0 0 1 1 1 1 are similar.

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Q: Suppose A is a symmetric matrix. (Au)" : u"A

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Q: uppose is the quadratic form Q = x Ax, where A is the symmetric matrix A = 2 he quadratic form is…

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Q: 3. Find all matrices which satisfy the matrix equation (::)(; })-(; :)(::)

A: Here,

Q: Let A be 3x5 matrix. Then AX=b has always infinitly many solutions.

A: Since not a particular question asked ,as per guidelines solution to first question is given below

Q: Determine whether or not the following sets S of 2 x 2 matrices are linearly independent s- {(; :)…

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Q: 4. Diagonalize the matrix, if possible. That is, find an invertible matrix P and a diagonal matrix D…

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Q: The equilibrium point of æ' = Ax + b is xo =-A¯'b for any matrix A. O True O False

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Q: 34. Is it possible for A³ to be an identity matrix without A being invertible? Explain.

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Q: Let A be a 5 x 3 matrix and assume that N(A) is trivial, i.e.. N(A) = {0}. Find dim C(A).

A: Given that A be a 5*3 matrix. and N(A)={0}. we have to find the dim C(A)?

Q: suppose an nxn matrix has positive diagonal entries and negative everywhere else. suppose sum of the…

A: Introduction: To prove that the determinant of matrix A is non-zero, we will show that A is…

Q: = = (*) (4) ¹9) 3x 5x-4x

A: Given that fxy=3x-y2x+y and gxy=3x5x-4y. We have to find the matrix A for f∘g.

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: The area of a square is given by 625xy. What is the length of one side of the square? O 25?xy O 25xy…

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Q: Can you show that Q is an intensity matrix?

A: Negative or non zero elements ,row sums adding upto zero and non negative off - diagonals elements.

Q: An mxn lower triangular matrix is one whos entries above the main diagonal are 0's. When is a sqaure…

A: when the diagonal elements are non-zero then the matrix is invertible. If all the diagonal entries…

Q: Find the adjacency matrix for C_4 *

A: We need to find the adjacency matrix of the cycle C4.