1.1 For the equations
x + y = 4, 2x - 2y = 4
draw the row picture and the column picture
1.2 for the system below, Show that the three columns on the left lie in the same plane, by expressing the third column as a combination of the first two.
Find all the solutions for b equals the zero vector
1.3 Apply elimination and back substitution
u-2v + w = 0
2v - 8w = 8
-4u + 5v + 9w = -9
1.4. which of the following are guaranteed to equal (A+B) ^2?
A^2+2AB+B^2
A(A+B+B(A+B)
(A+B) (B+A)
A^2+AB+BA+B^2
Does (AB)^2=A^2B^2
1.5 create a 3x3 elementary matrix that replaces row 2 with row 2 minus half of row 1
1.6 write the LU factorization of the system. use b=Lc and c=Ux to solve the system.
2x-y+2z=3
2x+2y-z=0
-x+2y+2z=-12
1.7
A =
A a a a
a b b b
a b c c
a b c d
Find four conditions on a, b, c, d to get A = LU with four pivots.
1.8 compute the inverse and transpose of the following matrix
2 3 0
1 -1 1
-1 6 4
1.9 compute the pivots in direct elimination to those with partial pivoting for
.001 0
1 1000