Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Matrix $A=\Bigg| \begin{matrix} 2 & 0 & 4 \\ -1 & -1 & -2 \\ \end{matrix}\Bigg|$ is a matrix of linear mapping $l: R^3\to R^2$ with the respect to bases $B = \{(1,0,0),(0,-1,1),(1,1,1)\}$ and $B' = \{(1,1),(1,2)\}$.

Find $l(1,2,3)$.

My result is $(7,-4)$, but I'm afraid I did some mistake. Could you, please, write your solution?

share|improve this question
    
Why don't you just check it? How would you go about checking it? –  k.stm Jan 20 '13 at 10:57
    
How am I supposed to check it? –  user50222 Jan 20 '13 at 11:04

1 Answer 1

up vote 2 down vote accepted

(1) Write $\,(1,2,3)\,$ as a linear combination of the given basis of $\,\Bbb R^3\,$:

$$(1,2,3)=a(1,0,0)+b(0,-1,1)+c(1,1,1)\,\,\,,\,\,a,b,c,\in\Bbb R$$

For example, $\,c=5/2\,$ ...

(2) Now just calculate

$$A\begin{pmatrix}a\\b\\c\end{pmatrix}$$

and get your vector...which is going to be given expressed in the given basis of $\,\Bbb R^2\,$, of course.

BTW, your result is correct.

share|improve this answer
1  
Addendum, @user50222: So you can use the coefficients of this vector to linearly combine the base vectors from $B'$ to a vector which should be … $(7,-4)$. –  k.stm Jan 20 '13 at 12:08

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.