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2.3hw - 2.3(Inst-mu ti o um TVMfl-fovmoiioh 3 —3 1 10...

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Unformatted text preview: 2.3 (Inst-mu ti o. um TVMfl-fovmoiioh) 3 —3 1 10. Use Fact 2.3.5; the inverse is —£5 5 e2 1 —2 1 20. Solving for 931,552, and 2:3 in terms of y1,'y2, and ya We find that 1:1 : '8'9'1 — 15112 + 1213 $2 : 4m + 5312 r 5.113 333 — —y1 — 312 + 93 w o 3 — It 26. Invertible, with inverse [2:1 5 [3/921 J1] 30. Use Fact 2.3.3: 0 1 b —1 o c ;{_1) 1 0 *0 1 0 —1 0 c 1J1? 0 1 b o 1 b —> 0 1 —b —r: a b. c o b -c 0 +b(1)+c(m 0 o This. matrix fails to be invertible, regarless 0f the values of b and c. 35. a. A is invertible if (and only if) all its diagonal entriesj a, d, and f, are nonzero. b. As in part (a): if all the diagonal entries are nonzero. (3. Yes, A”1 will be upper triangular as well; as you construct rreflAEIn], you will perform only the following row operations: a divide rows by scalars :- subtract a. multiple of the jth row from the 11th row, where j > 2'. Applying these operations to I”, you end up with an upper triangular matrix. (1. As in part (b): if all diagonal entries are nonzero. ...
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