Let TR R3 be the linear transformation given by X1 x2 T I3 == x4 3x19x25x3-7x4 - 9x5 2x16x23x3 -4x4-6x5 5x3 + 10x4 x5 (a) Find the image of T and find a basis for ImT. (b) Find the kernel of T and a basis for kerT. (c) Find the rank and nullity of T. Is the dimension of the domain of T equal to the sum of the rank and the nullity that you found?

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Q: Show that T is a linear transformation by finding a matrix that implements the mapping. Note that…

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A: The solution is posted below. Please go through it.Thank you Explanation:Step 1: Step 2: Step 3:…

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A: Solution is uploaded in next step

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Q: Let TR5 R³ be the linear transformation given by X1 x2 T x3 x4 X5 x1 + 2x2 x3 + 2x4x5 2x14x22x3 +…

A: ⎣⎢⎡​s+2t2s+5t2s​⎦⎥⎤​,s,t∈R⎣⎢⎢⎢⎢⎢⎡​x1​x2​x1​+2x2​+3x5​x5​x5​​⎦⎥⎥⎥⎥⎥⎤​,x1​,x2​,x5​∈R Nullity + Rank…

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