<p>I am taking a graduate linear algebra course and guess what, i remember about NOTHING from undergraduate linear algebra. This is the first week of class and i know some smarty in here knows how to do this stuff. HELP ME. </p>
<p>Consider the equation
y + 2kz =0
x + 2y +6z =2
kx +2z =1</p>
<p>a. for which values of the constant k does this system have a unique solution
b. when is there no solution
c. when are there infinitely many solutions.</p>
<p>Find the polynomial of degree 2 (a polynomial of the form F(t)= a + bt +ct^2) whose graph goes through the points
(1, -1)
(2,3)
(3,13)</p>
<p>note to others, do not wait 2 years to take a math course :(</p>
<p>The first question is easy.</p>
<p>Write the augmented matrix for the system of equations. Reduce to row echelon form. Then try to make the system consistent or inconsistent based on your choice if k. Let me know if you still can't get it and I'll do some of it.</p>
<p>For the second one, we set up the system:</p>
<p>y = ax^2 + bx + c</p>
<p>-1 = a + b + c
3 = 4a + 2b + c
13 = 9a + 3b + c</p>
<p>Solving for a, b, and c by setting up the augmented matrix and reducing to reduced-row echelon form will give you the polynomial...</p>
<p>i could have sworn i had to a determinant for the first one and than k would be apparent as to what it can or can not equal . at least that is what i did recently but i cant do the determinant normally for this matrix, always mess is up somehow.</p>