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PROBLEM 2.15] Consider the linear mapping T : R4 → R3, defined as T1 T2 | = 5x1 + 2x2 + 7x3 + 24 42:1 + 322 + 713-214 ) T4 (i) Write the corresponding matrix [T]. (i) Find a basis of Range(T).1 (ii Find a basis of Null(T).[1) (iv) Find the rank of T in 3 different ways.[1 (v) Show that T satisfies the rank theorem. 1

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T: R R3 52구 43子-2 3 The basis for range of dimenston of range of T-2Rank CT) The number of non zero rows n ref(7)=2= Rank( -

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