1 Let A be a 2 × 2 symmetric matrix satisfying A 9. and 2 -2] A 1 [1] with the spectral decomposition | A = 9 - n :- a [e Then: d The value of a is The value of b is The value of C is The value of d is

Q: A is a 4 by 4 matrix with 1 's on the diagonal and -a, -b, -c on the diagonal above. Find A - 1 for…

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Q: Find the spectral decomposition of the matrix 可

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Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: A square northwest matrix B is zero in the southeast comer, below the antidiagonal that connects (1,…

A: It's a very conceptual question and will need lots of grey matter. Please read the question…

Q: Define T:R³ R³ by T → Then we can write T(7) - D-[ Az where A- I1 - 23 11 + 312 - 13 12 +213

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Q: Suppose that A= det A-XI4 = 0. 42 0 4 02 -1 0 0033 04 0 7 . Find the eigenvalues of A, i.e. the A…

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Q: 1 1 -4 -2

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Q: Find the B-matrix for the transformation x Ax, when B = {b1, b2}. [ -1 4 3 b2 = A = b1 = -2 3

A: Given matrix, A=-14-23B=32-11

Q: -2 1 2 1

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Q: -5 4] -5 2 1 ||

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Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: Set up the matrix which will perform the following transformation and write down its character. (x…

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Q: Find the trace of the matrix 3 A 2 -2 tr(A)

A: The given matrix is A=-332-2. Find the trace of the matrix A as follows.

Q: Find the B-matrix for the transformation x-Ax when B=(b₁,b₂, b3}. A= -7 -72 1 17 -4 -72-21 The…

A: Solution :-

Q: -37 -1 0 -1 4 0 -1 -1 4 -1 0 A = 3

A: Here we use the gram Schmidt process to find the QR decomposition of matrix

Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: In Exercises 19-20, find the inverse of each of the following 4×4 matrices, where k₁, k₁, k3, k₁,…

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Q: 1 -2 A = -3 1 -1 -2 3 Let X such that AX = X A Find all 3x3 matrices Please show all steps. Thank…

A: Here the matrix A is given and we have to find the matrix X, such that AX = XA.   First calculate…

Q: Find the B-matrix for the transformation x-Ax when B= {b,, b2, bg). -8 -72 - 18 A= 1 16 5 b, b2 1 .…

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Q: Find the B-matrix for the transformation x+Ax when B = {b₁,b₂, b3}. 43 A = 1 20 -8-88-22 6, b₁ -4…

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Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: Find a 2 x 2 matrix such that -5 6 +988-0 1 -3 = [1 1

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Q: Find a 2 x 2 matrix such that -3 21 5 4 - 6 ปี

A: To find a  matrix such that

Q: 102 For A = [0 -1 2-2 -2 -2] find Q that diagonalizes this symmetric matrix. 0

A: Matrix diagonalization is a process used in linear algebra to transform a matrix into a diagonal…

Q: Use an inverSe matrix to Solve the given SyStem of epearkons. X, + X2=4 2X, - X2 -14

A: Here the given system is: x1+x2=42x1-x2=14 The system in matrix form can be written as:…

Q: Find matrix D such that D=2A+B-C

A: Given

Q: Let -1 2 -8 A = 1 0 0 1 Is A diagonalizable? If yes, find the matrix P that diagonalize A. Further,…

A: The given matrix is  A=-12-8010001

Q: Let A be the n × n matrix given by Show that det (A) = (a - 1) n − 1(a + n - 1)

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Q: [3 1 21 2 4 -1 6 0 2 -3 0 -1 0 3 A =

A: The element in the first row, second column of the matrix A is 0. So, we have to find the cofactor…