Find a real symmetric matrix. Q=xC_x_ such that where a) Q = x₁² + 2X₁ X₂ +3 x ²³² + 6 X₂ X ₂ + 2X₂³² x, ,,.b)...Q=. (26₂ - x₂) ²

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: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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Q: A is an n × n matrix with the property that A^2 = A. (a) If B = In − A, show that B^2 = B. (b) Show…

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Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

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Q: Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

A: To find: dimcol(A)⊥ Given information: A is 8×4 matrix such that rank(A)=3. Concept used:…

Q: For matrix (0 -1 0, 1 0 0, 0 0 1), show that [adj(A)}^-1 = (1 / det(A))*A = adj (A^-1)

A: The objective of the question is to prove the identity adj(A)^-1 = (1 / det(A))*A = adj (A^-1) for…

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: Find 3 x 3 upper triangular matrix with determinant 1.

A: 3×3 upper triangular matrix

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A: If  is a square matrix then its inverse is where

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

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: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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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: = = (*) (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: The symmetric matrix corresponding to the quadratic form X1 x2 = x} – 2x1x2 + 2x1x3 – 3x + 4x2x3 –…

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Q: please answer all thanks !

A: Step 1:Step 2:Step 3: