1 answer

Consider the system of lienar equations: ar +by = c dr + ey=f (a) Write the...

Question:

Consider the system of lienar equations: ar +by = c dr + ey=f (a) Write the above system in the form Arc = b (b) Show that th

Consider the system of lienar equations: ar +by = c dr + ey=f (a) Write the above system in the form Arc = b (b) Show that the system has a unique solution if and only if A has an inverse. Find the unique solution. (c) The corresponding homogenous equation is given by Az = 0 i.e. set the right hand side of the equation to zero). Show that the homogenous equation has a non-trivial solution if and only if A does not have an inverse. In this case, the solutions are either the entire plane or a line through the origin. (d) Determine h and k shuch that the solution set of system a) is empty, b) contains a unique solution, and c) contains infinitely many solutions: x1 + 3x2 = k 4.01 +h22 = 8

Answers

1 axtby = c } can be written an a dx tey = f f (ab 19 = 10) TA b) Let A has Invesse then AX = B ginn AT (AX) = A ZATA) X= ABd (131K 14ul & 13 | K Non-128-4k) (i) It has unique solution if det A to I det lo sell to > h 12 40 h $12 7) It has On finite

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