Suppose that A is a 6 X 6 matrix with characteristic polynomial cA(λ) = (1 + λ)(1 -λ)2(2 - λ)3• Prove that it is not possible to find three linearly in independent vectors v1, v2, v3 in R6 such that Av1 = v1, Av2 = v2, and Av3 = v3. (b) If A is diagonalizable, what are the dimensions of the eigenspaces E _1, E1, and E2?

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A: To Show: An orthogonal 2×2 matrix corresponds to a rotation in R2 if detQ=1, and reflection in R2 if…

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A: Introduction A square matrix is said to be an orthogonal matrix if…

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A: The given matrix is,A=123241-102

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A: IA is an invertible matrix To find det(AA-1)

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Q: 2. Let M2x2 (R) be the set of all 2 x 2 matrices (with real number entries). That is a b {[%] | a,…

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Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

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Q: 3 2 2 1 a) X1= b) Уi%3D| - 3 y2=| 1 X2= 3 X3= 1 4 y3= 1 3 1 N O

A: X=x1,x2,x3 be set of vectors. Let A=x1,x2,x3 and AT=x1x2x3 G=AAT where G is dram matrix. If G is…

Q: 9) please be clear with your answer, thanks!

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A: It is given that, A is a diagonalizable matrix with characteristicpolynomial.

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A: Basis of a vector space :                               A non empty sub set S be a basis of a…

Q: Q2/ Using Orthogonal Matrix 1 4 7, -8 4 If A = 4 prove that A- = A', A' being the transpose of A. 1

A: Solve by using the definition of the orthogonal matrix.

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A: Solution

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A: We are given that the non-zero vectors s(1), s(2), ..., s(n) are conjugate to a positive definite…

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Q: 10) Let A E Mnxn be given by 0 0 ao ... -1 .. A = -1 0 a2 .. 0 0 0 • -1 an-1 .. Compute XA(t).

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Q: Find the characteristic values and characteristic vectors of the matrix [8 − 6 2 − 6 7 − 4 2 − 4 3 ]

A: Consider the given matrix. A=8-62-67-42-43 Now, find the characteristic values.…

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A: Here we will prove the required result.

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Q: Consider a matrix A, its SVD is A = UZVH, where [300] -1/√2 0 0 1 1/√2 0 Σ -- 0 2 0,V: Lo o 1] -1/√2…

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Q: 2. Assume that A is a 3 × 3 matrix such that for 1 - (³).. ), j = 2 1 I 0 ;). it holds that Az = (a)…

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Q: 3. If A is a nonsingular matrix, then A' is nonsingular and its inverse is (A')1 = (A') '. Prove it!

A: A matrix A is said to be invertible if and only if  det(A) is not equal to zero i.e.  |A| ≠ 0