Assignment due Sep 9:

I have written up a description of the factorization of a
permuted arbitrary square matrix into a product of triangular
matrices.  It appears in the CLASS.110 directory.

READ IT.

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On Sep 2, the class constructed the following binary matrix:

011100
011101
001001  = A
101110
111100
011010

and the following 6-dimensional binary vector:

1
1
0  = b
1
0
1

Recall that the BINARY field has only two elements,
0 and 1, and that 1+1 = 0

Problem 1: For the 6x6 binary matrix, A, find a permutation
matrix P, a lower-diagonal matrix, L, and an upper diagonal
matrix U, such that PA = LU.

Problem 2: Find all 6-dimensional binary vectors which solve
the equation

	A x = b

(Hint: Write PAx = LUx = Pb.  First find all vectors y
such that Ly = PB, and then solve Ux = y.)

Problem 3: If possible, find another 6-dimensional binary vector,
c, for which the equation

	Ax = c has a different number of solutions than Ax = b.

Problem 4: How many different 6-dimensional binary vectors are
there in the column space of A?  In the null space of A?

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Read Sec 2.1 of the text.

Do the following exercises on pages 69-70:

2.1.5, 2.1.6, 2.1.7, 2.1.8, and 2.1.9.


Read Sections 2.2, 2.3, and 2.4

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