If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p2(x) as p(x) = P₁(x)p₂(x) then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x) = x² − 9, P₁(x) =x+3, p₂(x) = x − 3. -

Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

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Q: Let a and b be real numbers satisfying a² - a -1 = 0 and 6² - 36 - 2 = 0, and let V = 1 a b ab (a)…

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Q: For this exercise assume that the matrices are all nxn. The statement in this exercise is an…

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Q: 2 1 }], 3

A: LetWe have to find the inverse of the above matrix.We know that

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Q: Let A 1 2 −1 -2 3 -2 -1 1 1 Diagonalize A to find A100.

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Q: Find matrix X:   3.     6     5     4     -2   *X=     18     49     -20     6

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Q: Please write clearly. Thank you

A: a) To find the matrix A corresponding to the quadratic form: We need to identify the coefficients of…

Q: Suppose we are given A E Mmxn(C). How do the singular values of A relate to those of its adjoint, A*…

A: Please check step 2 for the solution.!

Q: Explain why v = ( 1, 0, -1) cannot be a row of A and also in the nullspace.

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Q: Let A, B, C square matrices of size 3 x 3. Find a counterexample to the following statements (you…

A: According to our guidelines, I solve first 3 subparts, so kindly request you repost the remaining…

Q: Given A = 1 0 0 -3 1 1 1 - 2 -1 " x = and b = 300 150 400

A: Given that the system Ax=bHere A=1-3101-201-1 , b=300150400

Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: Write f= x + 10x1x2 + x3 as a difference of squares, and f= x? + 10x,x2 + 30x as a sum of squares.…

A: Given f=x12+10x1x2+x22.  Let the associated matrix of f be A=abba is 2×2 symmetric matrix. Then,…

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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Q: Consider the quadratic form: =2x₁²-6x1x2+8x22 a. Find a matrix A such that q(x)=x Ax. You do not…

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Q: Suppose A is a 2 × 2 matrix, where -2 | u = Au = -4 A?u = 4 A³u 2 20 – 20 – 10. The minimal…

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Q: Consider the quadratic polynomial q(x) = 2x + 8x1x2 – 8x – 3x1 – 3x2 + 3. - - Find the symmetric…

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Q: as a polynomial in powers of (x - 1). p(x) = (x - 1)³+ (x - 1)²+ (x - 1)+ p(x) = -4x³ + 16x² - 24x +…

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