Let T: R² →→ R² where Find the matrix A such that T A = ([₁]) = ^ [²] · A T ( [7¹]) = [-53] and T -62 469 238

Q: The ODE (x dy/dx = yx²) is separable. true false If for a square matrix A and B, null matrix O, AB =…

A:

Q: Let A= 00 b) Say if A is diagonalisable sur Cv H E M3x3(C) such that H-¹AH is diagonal.

A:

Q: Verify Cayley-Hamilton theorem for the matrix A = and find its inverse. Also express A - 4A" 2 3 -…

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)…

A:

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

A:

Q: Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. How many relations are there from A to B?…

A:

Q: For matrix A and a scalar k, (kA)T is equal to: k(A^T) k(A) (k^2) x (A) (k^2) x (A^T)

A: We will solve the matrix operation.

Q: 2 1 Which of the following is the matrix C that satisfies the equality (CT- 412) 5 3 -1 (a) -5 (b) 1…

A:

Q: 8 = (²³). 21 Let A = Diagonalize A and use the diagonalization to calculate A¹00

A: Please find attachment

Q: T a(x¹ B) ax

A:

Q: Q6. Consider the function f: R³ R² defined by f((x, y, z))= (-2r, y + 32). (a) Show directly that f…

A:

Q: Write a'= -3x+y+ln(t), y'= t'a in matrix form as 18 31 and f(t) is 181 [*] -= P(1) [*] + f(t) where…

A:

Q: 1 2 A = 0 1

A: Given that A=1201 First to find the Jordan canonical form of this matrix: The given matrix is a…

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: EXER 7: MATRICES Prove that if N is invertible then MN¹ = N¹M if and only if MN=NM.

A:

Q: Determine the kernel and the range of the linear operator on L(x) = (x1 + x3, X2, 0)

A:

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

A:

Q: uppose is the quadratic form Q = x Ax, where A is the symmetric matrix A = 2 he quadratic form is…

A:

Q: 3. Find all matrices which satisfy the matrix equation (::)(; })-(; :)(::)

A: Here,

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

A:

Q: Suppose T: R¹→P3 is a linear transformation whose action on a basis for R4 is as follows: -3 0 ਏਕ ਦੇ…

A:

Q: 5) Find dx/dt of Matrix: X 5e-1 2e-¹ -7e-t

A: We know , d/dx(e-t) = -e-t   Given X = 5e-t2e-t-7e-t

Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1 AP =…

A: A square matrix A of order 2x2 is said to be diagonalizable if there exist an invertiable matrix P…

Q: Let J„ be the n × n matrix whose entries are all equal to 1, and let D(^1, ... , An) be the n × n…

A: The complete solutions are given below

Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1AP =…

A:

Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

A:

Q: Use matrix multiplication to find the dilation of (a, b) with factor k = α, where α > 1

A:

Q: -1 [A] = 4 3 -3 2 %3D L3 1] 2.

A: Given :                    2-134-32321 To find :                 The cofactors for C13 , C22 , C32…

Q: x 2y * (()) = (2+²) 4x 3. Let T a) T can also be written as T I ((₁)) = 4(3) A b. matrix you found…

A:

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: in

A:

Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

A: