Is 4x+2y=9 a linear equation

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

3 0

Yes it is a linear equation

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Orthogonalizing vectors. Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, a

jeka57 [31]

Answer:

$\\ \gamma= \frac{a\cdot b}{b\cdot b}$

Step-by-step explanation:

The question to be solved is the following :

Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if $b \neq 0$ . Recall that given two vectors a,b a⊥ b if and only if $a\cdot b =0$ where $\cdot$ is the dot product defined in $\mathbb{R}^n$ . Suposse that $b\neq 0$ . We want to find γ such that $(a-\gamma b)\cdot b=0$ . Given that the dot product can be distributed and that it is linear, the following equation is obtained

$(a-\gamma b)\cdot b = 0 = a\cdot b - (\gamma b)\cdot b= a\cdot b - \gamma b\cdot b$

Recall that $a\cdot b, b\cdot b$ are both real numbers, so by solving the value of γ, we get that

$\gamma= \frac{a\cdot b}{b\cdot b}$

By construction, this γ is unique if $b\neq 0$ , since if there was a $\gamma_2$ such that $(a-\gamma_2b)\cdot b = 0$ , then

$\gamma_2 = \frac{a\cdot b}{b\cdot b}= \gamma$

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3 years ago

What is the most abundant gas in the Earth's atmosphere?

butalik [34]

Answer:

Nitrogen

Step-by-step explanation:

Nitrogen and oxygen are by far the most common; dry air is composed of about 78% nitrogen (N2) and about 21% oxygen (O2). Argon, carbon dioxide (CO2), and many other gases are also present in much lower amounts; each makes up less than 1% of the atmosphere's mixture of gases. Hope this helped!

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3 years ago

Read 2 more answers

Which of the following shows 7 + (x + 4y) rewritten using the Associative Property of Addition? Select one: a. 7 + x + 4y b. 7x

ipn [44]

I'm pretty sure it's A. 7+x+4y, but I could be wrong.

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3 years ago

What are the solutions of the system? Solve by graphing. y=x^2-2x-1, y = -2

pychu [463]

I used desmos online.

(1,-2)

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