Homework 1, Due 11:59 P.M., Jan 14: CAPP 30271
Homework 1, Due 11:59 P.M., Jan 14: CAPP 30271
Homework 1, Due 11:59 P.M., Jan 14: CAPP 30271
, Jan 14
CAPP 30271
Reading
The reading corresponding to this homework is Sections 1.1–1.5 from “Linear algebra and its
applications” by David C. Lay, Steven R. Lay, and Judi J. McDonald, 5th edition. We will not
cover material from Sections 1.3 and 1.4 explicitly in class, so please read it on you own and
please ask if you face any difficulties.
• Suppose that A is the coefficient matrix for a system of four equations in six unknowns
and suppose that A has at least one nonzero row. (i) Determine the fewest number of free
variables that are possible. (ii) Determine the maximum number of free variables that are
possible.
2x + y + z = 1
6x + 2y + z = −1
−2x + 2y + αz = β.
1
Required Problems; submit
Please show your work clearly.
x + 2y + z = 0,
2x + 4y + z = 0,
x + 2y − z = 0,
x1 + 2x2 + x3 + 2x4 = 3,
2x1 + 4x2 + x3 + 3x4 = 4,
3x1 + 6x2 + x3 + 4x4 = 5.
4. Suppose the matrix A is such that two columns are the same: a3 = a4 . Argue why the
Gauss-Jordan procedure will find at least one nonbasic column in A.
5. Find the equation for a parabola, which has the form y = α+βx+γx2 that passes through
(0, 1), (1, 9), (2, 31) and (3, 63), if it is possible. Explain your answer.