Matrix Help: Understanding Parts (a) to (d)

[shermaine80]

Hi Guys,

I need help. I try out part(a) and (b).But it seem to me...my answer is not correct or too brief. Can anyone assist me? As for part (c). I'm not sure what A means here. Is it referring to A = [ cost -sint
sint cost]?
And what abt part (d), what does B means here? Can someone assist me how to do part (c) and (d)? Please advise. Thanks.

 

[radou]

What exactly is your problem? You should state it out more clear. I looked at the attachments and still didn't understand what you mean. Everything looks very clear.

 

[ppyadof]

For part a, have you considered multiplying the matrix you are given by the square of A?
As for c, A is simply the matrix of coefficients from the three equations which you are given in the question. The A in the equation does not refer to the A in the first part. Once you have A, find the inverse.
Part d, is almost the same as part c (but with a few changes).

 

[shermaine80]

Hi,

Is it possible to work out part (c) and (d) for me?
As i dun rele understand. Please advise. Thanks!

 

[HallsofIvy]

If you've seen any examples of changing systems of equations to matrix equations, c and d should be easy.

The first equation in c is 5x+ 5y- 10z= 0 which you can also write as 5x+ 5y- 10z+ 0w= 0 in order to include w. Remembering that you multiply matrices by multiplying "row times column", the first row of matrix A must be [5 5 -10 0] so that
$$\left[\begin{array}{cccc}5 & 5 & -10 & 0\end{array}\right]\left[\begin{array}{c}x \\ y \\ z \\ w\end{array}\right]= 5x+ 5y- 10z+ 0w$$

For part d, all that is different is that w has moved to the top of the array. That means it will be multiplied by the first column of the matrix B.

As far as part a is concerned, I would just multiply A¹⁰, which is given, by A twice more! I suspect you will need to use the "sum" formulas for sin(x+ y) and cos(x+y).

In b, (i), you say "there will be a solution if they intersect", iii, "multiple solution if they coincide", and for iv (I can't read the last part of ii) "no solution if the lines are parallel"

If what intersect? There certainly are no "lines" because this is not a two dimensional problem. You may be thinking of this as representing n "hyperplanes" but that is not given. The question is asking about the conditions on A and b.