Linear combinations of cash flows. we consider cash flow vectors over t time periods, with a positive entry meaning a payment received, and negative meaning a payment made. a (unit) single period loan, at time period t, is the t-vector lt that corresponds to a payment received of $1 in period t and a payment made of $(1 + r) in period t + 1, with all other payments zero. here r > 0 is the interest rate (over one period). let c be a $1 t − 1 period loan, starting at period 1. this means that $1 is received in period 1, $(1 + r) t −1 is paid in period t, and all other payments (i. e., c2, . . , ct −1) are zero. express c as a linear combination of single period loans.

Consider the following geometry problems in 3-space enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not work.) f equation editorequation editor 1. a plane and a line either intersect or are parallel t equation editorequation editor 2. two planes parallel to a third plane are parallel f equation editorequation editor 3. two lines either intersect or are parallel f equation editorequation editor 4. two planes orthogonal to a third plane are parallel f equation editorequation editor 5. two planes orthogonal to a line are parallel f equation editorequation editor 6. two planes either intersect or are parallel f equation editorequation editor 7. two lines orthogonal to a third line are parallel t equation editorequation editor 8. two lines parallel to a third line are parallel t equation editorequation editor 9. two planes parallel to a line are parallel f equation editorequation editor 10. two lines parallel to a plane are parallel f equation editorequation editor 11. two lines orthogonal to a plane are parallel