𝑇: ℝ3→ℝ3 defined by 𝑇(𝑥1,𝑥2,𝑥3)=(𝑥1+𝑥2,𝑥2+𝑥3,𝑥3+𝑥1).
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Expert's answer
2021-02-01T01:38:05-0500
T=⎝⎛101110011⎠⎞det(T)=1∣∣1001∣∣−1∣∣0111∣∣+0det(T)=2,then, T is invertibleAugmented matrix of T is,⎝⎛101110011100010001⎠⎞−R1+R3⟹R3⎝⎛10011−101110−1010001⎠⎞R3+R1⟹R1⎝⎛10001−111100−1010101⎠⎞R2+R3⟹R3⎝⎛10001011200−1011101⎠⎞21R3⎝⎛10001011100−2101211021⎠⎞−R3+R1⟹R1−R3+R2⟹R2⎝⎛1000100012121−21−21232123−2121⎠⎞T−1=⎝⎛2121−21−21232123−2121⎠⎞
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