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What is the solution to the following system? Is the solution unique? Use
the reduced row echelon form to explain why.
x + 2y + 3z = 1,
4x + 5y + 6z = 1,
7x + 8y + 9z = 1

Find the eigenvalues and eigenvectors for

A =
2 0.37 0
0 1.1 −4.29
1.6 0 2.2

Can you estimate the largest eigenvalues (in absolute value) using Power method for this
problem? Try to explain why if you can

Find the quadratic polynomial which interpolates (2, 0),(6, 1),(8, 0). Solve this with Maple. Start the problem by setting f(x) = ax2 + bx + c for example, then the unknowns are a, b, c.



A flate metal plate lies on an xy plane such that the temperature T at (x,y) is given by T=10(x^2+y^2)^2 , where T is in degrees and x and y are in centimeters.

Find the instantaneous rate of change of T with respect to distance at (1,2) in the direction of

a) the x-axis

b) the y-axis

How to get the equations of circles A, B, C, such as circle A with center (1,1) is drawn in the first quadrant.

Circle B with radius 2 and circle C are placed so that each circle is tangent to the other 2 circles and the x-axis.

THe 3 circles are on the first quadrant.

1) do it with Maple

2) do it by hand

3) draw the figure



N := 8;

b := 2 ∗ P i;
data := [];
for n f rom 0 to N do
data := [op(data), [n ∗ b/N, sin(n ∗ b/N)]];

Since exact points are not needed, changed the loop (and reinitialize) to:

data := [];

for n from 0 to N do
data := [op(data), [evalf(n ∗ b/N), sin(evalf(n ∗ b/N))]];

Modify the second example so that it can be used to graph the sin function
over any interval from a to b. (You should suppress the output from the for-loop in your
example, so that you do not fill up the worksheet with an unwieldy amount of output.)

I have a question that says write a procedure that takes a random graph and three edges of that graph and returns true if those edges share a common vertex. So I was thinking of something along the lines of

proc55 := proc (G, {a, b}, {c, d})

if evalb({a, b} = {a, c} or {a, b} = {a, d} or {a, b} = {b, c} or {a, b} = {b, d}) then print(true)

else print(false)

end if;

end proc;


I guess my main question is how do I put edges in the parameters line? It will let me write proc (G, a, b, c, d) but not proc (G, {a, b}, {c, d}).

Is there just something I'm missing or am I approaching this in the wrong way?


For the following maps, determine whether they are linear transformations or not, and present an
appropriate proof.

(a) T : R^4 → M2,3 given by T(a, b, c, d) =  [a   a^2   a^3
                                                                   b    c       d ]
(b) T : M2,3 → M3,2 given by T(M) = M^T (transpose of M)
(c) T : P3 → P3 given by T(p(x)) = p(2) + 3x · p'(x), where p'(x) denotes the derivative of the polynomial p(x).


i know that the 2 rules for proving are T (u+v)= T(u) + T (v) and T (ku)= k T (u).....but how do i show it with the questions above, like do i just take any numbers , so confused

Good day, can any one help in writing maple programme for the finite difference (FD) formulae define to solve this coupled non-linear  ODEs. See it here Thank you

NOTE: please disregard the earlier link.

Let Poly2 denote the vector space of polynomials

(with real coefficients) of degree less than 3.

Poly2 = {a1t^2+ a2 t+ a3 |a1; a2; a3 €R}

You may assume that {1,t; t^2}is a basis for Poly2.

(1) Show that L1 = {t^2 + 1; t-2 ; t + 3}and L2 = {2 t^2 + t; t^2 + 3; t}

are bases for Poly2.

(2) Let = 8t^2- 4+ 6 and = 7t^2- t + 9. Find the coordinates for

and with respect to the basis L1 and with respect to the basis L2

(3) find the coordinate change matrix P from the basis L1 to the basis L2.find P^-1

Just I answer part (1) can you help me to answer 2 and 3 

let A be a matrix=


[  7        7      9    -17

   6        6      1    -2

 -12    -12    -27    1

   7       7      17   -15 ]

What is the reduced row echelon form of A?

What is the rank of A?

A consistent system of linear equations in 14 unknowns is reduced to row echelon form. There are then 10 non-zero rows (i.e. 10 pivots). How many parameters (free variables) will occur in the solution?

Hello, I am a student typing up my homework assignments with maple, and I am takinng Inferential Statistics.  I can't figure out how to make the bar over a variable, so I can note the average.  It is just a line over a letter.  Kind of when notating a vector without the arrow.  It would be very helpful because I can't figure out how to make that symbol, it is not listed on the symbols list on the left side.


Hey guys! Can someone please help me by telling what I can insert into maple to get answer for this question? Thanks!

Is there any one to help me in calculating computational order of convergence of derivative free method. I am trying to calculate programs runs with immature error and does not print it.

Please is there any 1 to help.


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