Math Is Fun Forum

!nval!d_us3rnam3

Member

Registered: 2017-03-18

Posts: 46

More Vectors and Matrices (urgent)

(a) Let

and let

Show that

sends each of

and

to scalar multiples of themselves, and find the value of these scalars.

(b) Let

be a positive integer. Use part (a) to find the vectors

(c) Write the vector

as a linear combination of

and

.

(d) Using parts (a), (b), and (c), calculate

I need to write a detailed solution for all four of these; if you could walk me through that, that would be great. Thanks!

Last edited by !nval!d_us3rnam3 (2019-06-19 07:14:13)

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zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: More Vectors and Matrices (urgent)

For part (a), what happens when you multiply that matrix by each of those vectors?

For part (b), you'll have been able to find some number

(called a 'scalar multiple') such that

, and likewise for the others. This then tells you that

. Use this to write down an expression for

and therefore

.

For part (c), trial and error is easiest here: try to find a way of making 10 from a linear combination of

and

. Then see if that same linear combination works for the other two vector components.

For part (d), you can use your linear combination found in part (c) to replace that vector with something that looks like

. You can then split the matrix multiplication into three parts: can you see how?

Jaspers

Member

Registered: 2019-05-24

Posts: 54

Re: More Vectors and Matrices (urgent)

Hi !nval!d_us3rnam3.

Another way you can do part (c) is to let

from which you get the system of linear equations

from which you can easily solve for x, y, z.

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