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?
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?
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 $(a+d) + (b +e) - 2(c + f)$?