assign3-for_posting - C Is the fourth column of C an...

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Math 136 Assignment #3 Winter 2008 Due Date: 8:30 a.m., January 30, 2008. 1 If a system of two equations in three unknowns has a solution, explain why there is more than one solution. 2. Find (if possible) the conditions on a and b such that the system of equa- tions given below has no solutions, exactly one solution or an infinite number of solutions ax + y = - 1 2 x + y = b 3. Let C = 2 - 4 - 18 - 18 1 - 3 4 2 - 3 8 1 5 . (a) Find a row-reduced echelon matrix which is row equivalent to C . (b) Regarding C as the augmented matrix of a linear system, which are the pivot columns of C ? (c) Does the system in (b) have no solutions, or exactly one solution or in- finitely many solutions? Explain. (d) Consider the column space formed by the first three columns of
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Unformatted text preview: C . Is the fourth column of C an element of this column space? If so, exhibit this fourth column as a specific linear combination of the first three columns. If not, explain why not. (e) Change the ”5” in the third row, fourth column to ”6”. Repeat the pro-cedure of 3(d) with this change. (f) Suppose C is the coefficient matrix of a homogeneous system. Determine the null space (solution space) of C . 4. Using row reduction, and specifying the operations used, show that the following linear system has a unique solution and determine that solution. x + 2 y + z = 11-x + y-z =-5 4 x-y + z = 14 1...
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