Question

6. Is the transformation T: R → R defined T(x, y) = (x + y, x - y + 1) a linear transformation? [3 marks]

8. Let A = 5 6 Find the eigenvalues and ONE of the corresponding 21 eigenvectors of A. [5 marks]

please answer both!! thank you

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Answer #1

2 6) T: IR?, IR? T:1R2_air² is we know linear toces formation =(x1+41) +(het 42, (21-4, +1 +82-4271 T(X4) is not linear toces$) A=[: 5 6 To find eigen value. consider 1 A-d I) 20 |(343-2[%]) = 1** - ے a (5-2)(1-4) -122 5-5d-d+12_12=0 d²6d-7=0 (1-7)(117:10 J Tay] =10] 2 6 2 -6 R2 R₂+RI kunc 6][7.]=[0] system has infinite solh. put 22=1 -22, +6=0 . 21 = 3 3 corresponding ei

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please answer both!! thank you 6. Is the transformation T: R → R defined T(x, y)...
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