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.

M = \begin{bmatrix} a & b \\ c & 0 \\ \end{bmatrix}

with $a + b - 2c = 0$

Show that M is a subspace from $M_{2:2} (\mathbb{R})$

[$M_{2:2} (\mathbb{R})$ is the ring of 2 \times 2 matrices over the real numbers]

can someone help me?

share|improve this question
2  
Since you are new to this site, please consider reading this: How to ask a homework question?. In particular, you should use homework tag if your question comes from a homework. I wrote this comment because the question sounds homework-like. –  Belgi Oct 30 '12 at 5:58

1 Answer 1

To show $M$ is a subspace, you need to show that $M$ is closed under addition and scalar multiplication.

Scalar Multiplication: $$k\begin{bmatrix} a & b \\ c & 0 \\ \end{bmatrix} = \begin{bmatrix} ka & kb \\ kc & 0 \\ \end{bmatrix}$$ Since we know $a + b - 2c = 0$, what can we say about $ka + kb - k2c$?

Addition: $$\begin{bmatrix} a & b \\ c & 0 \\ \end{bmatrix} + \begin{bmatrix} d & e \\ f & 0 \\ \end{bmatrix} = \begin{bmatrix} a +d & b+e \\ c+f & 0 \\ \end{bmatrix}$$ This time we know that $a + b - 2c = 0$ and $d + e - 2f = 0$. So what can we say about $(a+d) + (b +e) - 2(c + f)$?

share|improve this answer
    
im sorry for Belgi... This is my homework. sorry if you feel uncomfortable –  Zuhair Oct 31 '12 at 0:47
    
thanks for Deven Ware... your answer help me... –  Zuhair Oct 31 '12 at 0:47

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.