3.Let1 2-2 263T=3 451-1 1Determine whether T is linearly independent in the vector space M2,2(R) of all 2 x 2 matriceswith coefficients in R.

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Answered: 3. Let {[ 1 2 -2 2 6 3 T = 3 4 5 1 -1 1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3: Which of the following sets are closed under scalar multiplication? (1) The set of all vectors in R of the form (a, b, 9ab). (i1) The set of all polynomials a- bx+ cx in P, such that ac =D0. (iii) The set of all matrices in Mn such that A = A (A) (1) and (ii) only (B) (1) and (iii) only (C) (ii) and (iii) only (D) (1) only (E) (ii) only (F) none of them (G) (iii) only (H) all of them
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3. Let {[ 1 2 -2 2 6 3 T = 3 4 5 1 -1 1 Determine whether T is linearly independent in the vector space M2.2(R) of all 2 × 2 matrices with coefficients in R.