5. Consider the linear transformations T: R R and S: R 1 R with matrices: 1...

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5. Consider the linear transformations T: R R and S: R 1 R with matrices: 1 0 1 ++ - ( ) + - ( 1 ) -3 6 AT = As -1 10 3 0 2 Find the null space of T, N(T), and the range of T, R(T). Describe each subspace or write down a basis. Do the same for the null space of S, N(S) and the range of S, R(S). Which linear transformation is defined: ST or TS? Deduce the null space of the composed linear transformation. Use the rank-nullity theorem to find the dimension of the range of the composed linear transformation. (20 points) 5. Consider the linear transformations T: R R and S: R 1 R with matrices: 1 0 1 ++ - ( ) + - ( 1 ) -3 6 AT = As -1 10 3 0 2 Find the null space of T, N(T), and the range of T, R(T). Describe each subspace or write down a basis. Do the same for the null space of S, N(S) and the range of S, R(S). Which linear transformation is defined: ST or TS? Deduce the null space of the composed linear transformation. Use the rank-nullity theorem to find the dimension of the range of the composed linear transformation. (20 points)

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Solution 1 Given A 2 3 64 3 1 3 i The reduced row echelon form of 4 is 2 So The RREF conatians 1 non... View the full answer