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orange12
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Let the vectors a1,a2,a3 €R3 and b1,b2,b3 € R4 be given by
a1 a2 a3
1 -2 3
2 2 1
1 1 2
b1 b2 b3
1 1 -1
2 -3 2
1 4 3
3 -2 1
The linear transformation S : R3 --> R4 is defined by
S(x)= b1a1Tx+b2a2Tx+b3a3Tx x€R3
1. Find the standard matrix A for the linear transformation S og decide if the linear transformation S er injective or surjective.
a1 a2 a3
1 -2 3
2 2 1
1 1 2
b1 b2 b3
1 1 -1
2 -3 2
1 4 3
3 -2 1
The linear transformation S : R3 --> R4 is defined by
S(x)= b1a1Tx+b2a2Tx+b3a3Tx x€R3
1. Find the standard matrix A for the linear transformation S og decide if the linear transformation S er injective or surjective.