Problem 3.3. For the following vector spaces V and maps : V → V prove that they are linear, and write their matrices in

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Problem 3 3 For The Following Vector Spaces V And Maps V V Prove That They Are Linear And Write Their Matrices In 1 (64.57 KiB) Viewed 28 times

Problem 3.3. For the following vector spaces V and maps : V → V prove that they are linear, and write their matrices in the indicated basis of V a) 6 : R³ → R³, 6(x, y, z) = (3x − y + 2z, −x − y + z, −2x + y − 4z); standard basis of R³. b) þ : R³ → R³, is the rotation with respect to the x-axis by 60 degrees counterclockwise; standard basis of R3 c) V is the space of all polynomials of degree at most n, ¢(P(x)) = P'(x)+2P(x); basis (1, x, E², E³ 27).