The linear transformation T : R4[x] → M2×2(R) has matrix(1 1 2 2 1'1 21 31 413 35 4-15 7with respect to the standard basis (1, x,x², r°, x*) for R4[x] andfor M2x2(R).a) Find a basis for Range(T).b) Find a basis for Ker(T).

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The linear transformation T : R4=) → M2×2(R) has matrix (i 1 2 2 1) 1 2 3 3 |1 30 5 4 (1 4 -1 5 7) 1 wvith respect to the standard basis (1,1, r², r²,r*) for R4[#] and m) Find a basis for Range(T). b) Find a basis for Ker(T).

The linear transformation T : R4=) → M2×2(R) has matrix (i 1 2 2 1) 1 2 3 3 |1 30 5 4 (1 4 -1 5 7) 1 wvith respect to the standard basis (1,1, r², r²,r*) for R4[#] and m) Find a basis for Range(T). b) Find a basis for Ker(T).

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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Question

The linear transformation T : R4[x] → M2×2(R) has matrix
(1 1 2 2 1'
1 2
1 3
1 4
1
3 3
5 4
-1
5 7
with respect to the standard basis (1, x,x², r°, x*) for R4[x] and
for M2x2(R).
a) Find a basis for Range(T).
b) Find a basis for Ker(T).

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