Find the matrix C' of the linear transformation T(x) = B(A(x)). C = || A = [1] [85] А and B = 3

Q: 3 х. 0 -2 T(x) %D Find the matrix M of the inverse linear transformation, T-1. M =

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Q: We consider the linear transformation T : R3 ------R 3 T(x,y,z) = ( x+2y-z, -x+y+2z, 3z) 1. Give the…

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Q: Find the matrix M of the linear transformation T: R³. →>>> R² given by X1 (J- = -3x1 - x2 + 9x3 2x1…

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Q: 4. Let T: R" → Rm be a linear transformation and suppose T(u) = v. Show that T(-u) = -v.

A: Since T is a linear transformation, for any scalar number c, we must have,        T(cu) = cT(u)

Q: Find the matrix M of the linear transformation T : R3 → R2 given by () [ = M: T -9x1 + x2 + (-4)x3…

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Q: 4. Consider two 3 × 3 matrices A and B with det(A) = -2 and det(B) = -1. Let T(*) = Až be a linear…

A: solution :-

Q: 11. Find the standard matrix of each of the following linear transformations on R². x * ([1]) -…

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Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

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Q: Find the matrix M of the linear transformation T: R → R' given by [821 + (-8)2] 7(E) - 711 + 12 M =

A: The solution is given as

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

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Q: Determine whether the following are linear transformationsfrom P2 to P3. L (p(x)) = p(x) + xp(x) +…

A: Given : Lpx=px+xpx+x2p'x To Determine : L is linear transformation

Q: Find the standard matrix for the linear transformation T. T(x, x2) = (0, 0)

A: Solution

Q: A B -2 -2

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Q: Let T: R³ → Rº be a linear transformation defined by T'(x) = Ax where the matrix ;] A = -1 -1 -1 0 2…

A: Find the answer below.

Q: Let A = and B = 4 Find the matrix C of the linear transformation T(x) = B(A(x)). C =

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Q: Let T: R² → R³ and S: R³ → R² be two linear transformations. Suppose the matrix of T is 21 -1 and…

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Q: Let Find the matrix C of the linear transformation T(z) = B(A(z)). C ^-6 87 A and B =

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Q: [102] 6. Find the kernel of the linear transformation whose standard matrix is B= 215. [237]

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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: Consider the linear map T : R² → R² which sends (1,0) → (-3, 5) and (0, 1) → (4, –1). (a) What is…

A: Follow step 2.

Q: = (5) Find the standard matrix for the transformations T₁(x, y) (x - 2y, 2x + 4y) and T₂(x, y) = (x…

A: This is a linear algebra question. The standard matrix is find with respect to the standard basis.

Q: Find the standard matrix for the linear transformation T. TN, Y, 2) - (x+ 1,x-Y. 2-x)

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Q: T(xy)=Cax?+by?, cx²+dy²) 2

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Q: If T1 = a1(d/dt)² + b1 (d/dt) + cqI %3D and T2 = a2(d/dt)² + b2(d/dt) + c2I are linear…

A: Linear transformations do not satisfy the commutative law . Because a linear transformation T is…

Q: ppose that T : R² → R² is a linear transformation and that 7([일) -B] T and ar (H) nd T

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Q: linear transformation A maps P(1,0) to P’(-2,-4) and Q(0,1) to Q’(4,1). Find (i) The matrix A (ii)…

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Q: (6) Let T : R² → R³ be the linear transformation defined by - (E)-E [2(x1 – x2)] x2 – 3x1 x1 + x2 |…

A: That's easy. Have a great day!!!

Q: [1 The columns of 3 = 0 O Suppose that T is a linear transformation from R³ into R² such that T(e₁)…

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Q: 3. Each of J, K, L, M and N is a linear transformation from R' to R?. These functions are given as…

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Q: (а) T(г, у) — (т, -у); (b) T(г, у) — (2г, 5у): (с) T(т, у) — (т+у, y):

A: We have to find the canonical form of the linear transformation. We choose the canonical basic for…

Q: M Find the matrix M of the linear transformation T: R² → R² given by 4x1 T ([2]) = [¹²2² + (-5) ²].…

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Q: A 3 T = (l:))-I:1. "(;)) T Consider a linear transformation T from R³ to R2 for which 0 8 (A) - (A)…

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