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There is no one-to-one linear transformation
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- Fully solvearrow_forwardDetermine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) If T: Rn→Rm is a linear transformation such thatT(e1) = [a11 a21 . . . am1]TT(e2) = [a12 a22 . . . am2]T ⋮ T(en) = [a1n a2n . . . amn]T then the m × n matrix A = [aij] whose columns correspond to T(ei) and is such that T(v) = Av for every v in Rn is called the standard matrix for T.(b) All linear transformations T have a unique inverse T−1.arrow_forward(a) Evaluate S(3, 1, −2). (b) Evaluate S(S(3, 1, −2)). (c) Evaluate S(2a, 3a + b, b − 2a), where a and b are arbitrary real numbers.arrow_forward
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