HOMEWORK #1 due 1-29
NOTE: In the following, _ means subscript and ^ means superscript. The expression Sum(i=a,b) h(i) (for example) means the same as Sumi=1b h(i), which is the sum of h(i) for i=a,a+1,...,b. Also, ``ne'' means ``not equal to'', so that x ne 0 means that x is not equal to zero.
1. Find all solutions x,y of the following two linear equations by elimination
x - 4y = -10
3x - 8y = 30
Be careful!
2. Find all solutions x,y,z of the following three linear equations by elimination
3x + 6y + 9z = -18
2x - 3y - 4z = 15
3x + 4y + 5z = -8
(Be careful on any homework problem.)
3. Find all solutions x,y,z of the following three linear equations by elimination
x + 2y + z = 4
x + y + 2z = 8
x + 4y - z = 5
Be careful! Remember that a system of linear equations may have no
solutions at (that is, is inconsistent), or else may have may
different solutions, in which case you are asked to find them all,
perhaps in terms of a free variable on which there are no constraints. If
you can show that the system has no solutions at all, just say so and give
a reason.
4. Assume that
[ a+b c-d ] = [ 8 2 ] [ c+d a-b ] = [ 4 6 ]What are the values a,b,c,d?
5. Assume that
A = [ 2 4 ] and B = [ 1 3 ]
[ 4 -1 ] [ 5 -1 ]
[ 5 7 ]
6. (Slightly harder than the others.) Consider the matrix
A = [ 1 3 7 ]
[ 2 6 14 ]
[ -1 -3 -7 ]