Systems with a parameter

units
abc
abc
abc
vector
logic
function
standard

abc

↵

(

)

↑

←

↓

→

units
abc
abc
abc
vector
logic
function
standard

shift

greek

↵

(

)

↑

←

↓

→

units
abc
abc
abc
vector
logic
function
standard

shift

greek

↵

(

)

↑

←

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→

units
abc
abc
abc
vector
logic
function
standard

−

×∗×

√

a■

{......

[

]

∞

{}

det

(m×n)

↵

(

)

↑

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→

units
abc
abc
abc
vector
logic
function
standard

∧

⊥

∀

⊢

∅

∪

⊂

∨

⊤

∃

≠

⊨

∈

∩

⊆

∄

→

□

⊕

≥

∖

∉

⇒

⊬

⊃

↔

◇

⧆

≤

⊭

≡

{}

⇔

⊇

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(

)

↑

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units
abc
abc
abc
vector
logic
function
standard

−

×∗×

√

a■

log

sin

[

]

cos

lim

∞

[

)

≥

tan

(

]

≤

arc

{......

(

)

↵

(

)

↑

←

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→

units
abc
abc
abc
vector
logic
function
standard

−

×∗×

√

a■

log

sin

∧

cos

∨

≥

tan

all

≤

none

↵

(

)

↑

←

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→

units
abc
abc
abc
vector
logic
function
standard

°C

mol

bar

rad

units

↵

(

)

↑

←

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units
abc
abc
abc
vector
logic
function
standard

−

×∗×

√

a■

log

sin

∧

cos

∨

≥

tan

all

≤

none

↵

(

)

↑

←

↓

→

Consider the following set of linear equations with unknowns $x$ and $y$ at different values of the parameter $a$ .

$\left\{\begin{aligned}\phantom{2}x+2 y &=0\\ 2x+ay &=1\end{aligned}\right.$

For what value of $a$ is there no solution?
If the system is solvable, what is the solution?

1. For $a=\;{}$

$\phantom{x}$ there is no solution.

2. If the system solvable, then the solution is $\cv{x\\y}=\;{}$

$\cv{\Box\\ \Box}$

Systems of linear equations: System of linear equations and matrices

Systems with a parameter