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For problems 1-4 the linear transformation T/; R^n - R^m  is defined by T(v)=AV with A=[-1 -2 -1...

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Basic Math

For problems 1-4 the linear transformation T/; R^n -R^m  is defined by T(v)=AV with

A=[-1 -2 -1 -1

2 1 0 -4

4 6 1 15]

1.   Find the dimensions of R^n and R^m (3 pts)

2.   Find T(<-2, 1, 4, -1>) (5 pts)

3.   Find the preimage of <-6, 12, 4> (8pts)

4.   Find the Ker(T) (8 pts)

Answer & Explanation Solved by verified expert
3.9 Ratings (428 Votes)
T Rn Rm is defined by TV Av where A 1 2 1 1 2 1 0 4 4 6 1 15 1 Since A is a 3x4 matrix hence it can be multiplied to the right only by a 4vector and the result will be a 3vector Hence n 4 and m 3 2 Let    See Answer
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