2. factor 1/4, then reflects about the line y = x. = (1/4 ( (a) A Find the standard matrix for the operator on R² which contracts w (d) A = 1 1/4 0 ) 0 1/4 1/4 0 0 - (1¹/4) 0 (e) None of these (b) A = (c) A = (!)

Q: [a11(t) a12(t) 1) Let A(T) = be differentiable. %3D Show that: d (det (A(t)) = det a 12 (t)] la21(t)…

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Q: erify the Cayley-Hamilton Theorem for a general 2 x 2 matrix A, a b -[1]. For a nonsingular n x n…

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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: 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: Find the matrix A of the linear transformation from R² to R³ given by 1 0 -8 x2. -4 x1 + 2 -6 T…

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Q: (4) Given a matrix X of independent variables, psudo-inverse X† is defined as (X"X)-'x" (a) If X is…

A: If a matrix is of order (mXn) then transpose of A is of order (nXm).

Q: Find the transformation matrix for the following figure: B'(-5,3) A(-5,0) C(-3,0) B(-5,-3) A(-3,-3)

A: Given the triangle A(−3,−3),B(−5,−3),C(−3,−6).We need to find the transformation matrix so that we…

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: Solve for x and y in the matrix A=[x 3 2 y] if A^2 = [ 31 12 8 87] x = y =

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Q: 8 Consider a square matrix B whose inverse is given by B'. a In terms of B", what is the inverse of…

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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: = = (*) (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: a) Let A and B be two regular (nonsingular) (n, n)-matrices. Determine whether the following is…

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

A: The given matrix is,  A = diag(-2, -1, 2). We have to put the following quantities in increasing…

Q: Given F(x) = 4₁ 21 -2x1 3 4x2 3 2x1²x24 2x15x2 calculate the matrix Jp ([^])

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Q: (ЗАТ + 4CТВ)Т- 54 - 4B

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Q: Use determinant to find the equation of the line that passes through the points (4, ― 3) & ( ―1,2)

A: We have to find equation of line using given information Concept required: Equation of line passing…

Q: (BH) Recall that a matrix Q is orthogonal if Q' Q = I.

A: Given, A matrix Q is orthogonal if QTQ=I Proof: (a) The one way to write the norm for vector x is…

Q: The matrix that projects onto the line y = 1 2 8 is X 0.6 0.8 0.8 -0.6

A: Let  be projection on the line Then  is  a linear transformation with matrix