- Algebra Lineal - 2da Edicion - David Poole. Algebra Lineal y sus Aplicaciones - David C. Si se puede necesito el solucionario de algebra lineal de bernard.
- Lay is also co-author of several mathematics texts, including Introduction to Functional Analysis, with Angus E. Taylor, Calculus and Its Applications, with L.J. Goldstein and D.I. Schneider, and Linear Algebra Gems-Assets for Undergraduate Mathematics, with D. Johnson, and A.D.
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7.1 SOLUTIONS
AIgebra Iineal y sus aplicaciones, 4ta Edicin David C.
Notes: Students can profit by reviewing Section 5.3 (focusing on the Diagonalization Theorem) before working on this section. Theorems 1 and 2 and the calculations in Examples 2 and 3 are important for the sections that follow. Note that symmetric matrix means real symmetric matrix, because all matrices in the text have real entries, as mentioned at the beginning of this chapter. The exercises in this section have been constructed so that mastery of the Gram-Schmidt process is not needed.
Theorem 2 is easily proved for the 2 2 case:
If ,a b
Ac d
= then ( )2 21 ( ) 4 .2 a d a d b = + + If b = 0 there is nothing to prove. Otherwise, there are two distinct eigenvalues, so A must be diagonalizable.
In each case, an eigenvector for is .db
1. Since 3 5
,5 7
TA A = = the matrix is symmetric.
2. Since 3 5
,5 3
TA A
= the matrix is not symmetric.
3. Since 2 2
,4 4
TA A = the matrix is not symmetric.
4. Since 0 8 38 0 2 ,3 2 0
TA A
= =
the matrix is symmetric.
Algebra Lineal David C Lay Solucionario Con
5. Since 6 2 00 6 2 ,0 0 6
TA A
=
the matrix is not symmetric.
David C Lay Linear Algebra
Algebra Lineal David C Lay Solucionario En
6. Since A is not a square matrix TA A and the matrix is not symmetric.