Using matrix multiplication and the matrix representation of R(0), prove that the R-'(0) = R(-0) (Hint: you need to show that R(0)-R(-0) = R(-0)·R(0) = I where I is the identity matrix.

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: Find the characteristic polynomial of the matrices

A: we have to find  the characteristic polynomial of the matrices A=21-13

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: 2 1 Let A = Show the details of two different methods [(1) using the adjoint and determinant, (2)…

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Q: 29. Determinant of an Inverse Prove for invertible matrix A that

A: To prove: A-1=1A

Q: (il,if i = j A = + 1)',if i = j B = if i + j +1if i #j

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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: Suppose that T : R² → R² is a matrix transformation and that 7([}))-[-), "([;))-}] 7((:) (a) Find…

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Q: (a) If A and C arenxn matrices with C invertible, prove that: det (C-AC) = det(A). (b) Given that…

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Q: Show that if annxn matrix U satisfies (Ux)· (Uy) = x•y for all x and y in Rn, then U is an…

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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: Find a matrix corresponding to the linear transformation that rotates R clockwise by 45 degrees…

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Q: (b) Prove that the following matrices are symplectic : (i) (ii) [1] matrix. where I is the nxn…

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Q: Find the determinants of the following matrices and classify them as either singular or non…

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Q: If Aand B are invertible matrices of the same order, Then show that AB is invertible matrices.…

A: LHS   =  (AB)-1  RHS  =  B-1A-1 For    (AB)-1  =  B-1A-1 ,   RHS * inverse of LHS = i…

Q: *(})- (;) -(;) 1 3

A: T:R2→R3 satisfying the condition, T11=121 and T12=132

Q: 0 1 1 (₁2) (₁) (1₂) Calculate matrix = = (A – AT)² and vector w = Bx. Then, Consider matrix A = X =…

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Q: Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix…

A: As per guidelines of bartleby we solve only first three parts.

Q: (1 point) The matrices - [8]. [J]. -[i]·.^ - [i]· A A4 = A₁ = A3 = A₂ = form a basis for the linear…

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Q: Orthogonally diagonalizable the following matrix 2 1 1 C = -1 1 1 0 -1 1.

A: The solution is below.

Q: Prove det(A) = det(A'), for an upper triangular matrix A.

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Q: Let 0 3 0 1 1 2 2 1 A = -1 B : 0 1 1 2 0 1 -2 Compute det(AB), det(A-'B-!) and det(2A) where 2A…

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Q: f (x1,X2,x3) = xỉ + 3x1x2 – x2X3 +x3 – 4x3 Rewrite f in the matrix form x'Ax where A is a symmetric…

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Q: Assuming that all matrices are n x n and invertible, solve for D. CAB DAC'B = CA". D=…

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Q: Consider the transformation T: R -R' given by T(x,X.a) (x +8x. 0, 3r,+X x,-x). Find the standard…

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Q: (c) For the real symmetric matrix A, find a non-singular matrix P such that PTAP is diagonal and…

A: Given: A matrix defined as .Aim: To determine the matrix , such that is a diagonal matrix. Also…

Q: Show that ||A||2 =  √(ρ(AA*))  where ρ(AA*) is the spectral radius of the AA* matrix.

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Q: 3) Find a sequence of elementary matrices whose product is A and a sequence whose product is A'. - 3…

A: We have to find a sequence of elementary matrices E1 , E2 , E3 etc. such that  product of elementary…

Q: Let A and B be 4x4 matrices such that det(A) = 5 and det(B) = 3. Compute the determinant of…

A: Explanation of the answer is as follows

Q: Let T: R³ → R² be defined by T -~--~--E) ----B]}~~(~-| ||-~ ~[]) Let B = u₁ U3 = { = [3], , = 6 (ED)…

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