Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphisms.
11.
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- Let T be a linear transformation from P2 into P2 such that T(1)=x,T(x)=1+xandT(x2)=1+x+x2. Find T(26x+x2).arrow_forwardFor the linear transformation T:R2R2 given by A=[abba] find a and b such that T(12,5)=(13,0).arrow_forwardFind the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forward
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- II. Let V =span- and define the transformations [a b] c d [a² – 6? c? - d²1 S(A) = adj(A) d Determine which transformations are linear. i. T: M2x2(R) → M2x2(R) ii. S: M2x2(R) → M2x2(R) iii. T :V → M2x2(R)arrow_forwardDetermine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(X1,X2,X3,X4) = (X2 + X3,X2 + X3.X3 + X4,0) a. Is the linear transformation one-to-one? O A. Tis one-to-one because T(x) = 0 has only the trivial solution. O B. Tis not one-to-one because the standard matrix A has a free variable. O c. Tis not one-to-one because the columns of the standard matrix A are linearly independent. O D. Tis one-to-one because the column vectors are not scalar multiples of each other. b. Is the linear transformation onto? O A. Tis not onto because the columns of the standard matrix A span R4. B. Tis onto because the columns of the standard matrix A span R4. OC. Tis not onto because the fourth row of the standard matrix A is all zeros. O D. Tis onto because the standard matrix A does not have a pivot position for every row.arrow_forwardDraw the image that satisfies the following. Parallelogram EFGH is the output of the transformation as defined below. DEFGH = Ro(OABCD) Draw DEFGH. 2 PENCIL 19 -B 7 THIN -6 33 4 3 BLACK Hut 2 1 STY 8 7 6 5 EL 1 2 #H 1 7 3 + 15 6 -7 NO 1 B 2 4 6 7 8 H D Carrow_forward
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