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4 years ago

Express 80 as a product of prime factors using index notation

Mathematics

1 answer:

hammer [34]4 years ago

4 0

80 = 2 x 2 x 2 x 2 x 5
80 = 2 ^4 x 5

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What is the measure of angle 1?

lbvjy [14]

Answer:

70 degrees.

Step-by-step explanation:

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This is the last question i need help on! i will mark brainlessttt :)thanks

Mandarinka [93]

Answer:

A.3

Step-by-step explanation:

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4 years ago

How to factor this equation.<br><br>n^2-64

stellarik [79]

$a^2 -b^2 = (a+b)(a-b)

$
i would suggest memorizing this

hence
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3 years ago

What is the slope of the line with the equation of y = =*

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3 years ago

T(v) = Av represents the linear transformation T. Find a basis for the kernel of T and the range of T.

lawyer [7]

Answer:

Ker(T) has basis $\emptyset$

Range(T) has basis $\left\{\left(\begin{array}{c}2&3\end{array}\right), \left(\begin{array}{c}1&4\end{array}\right) \right\}.$

Step-by-step explanation:

If the matrix you wanted to represent is $A=\left(\begin{array}{cc}2&1\\3&4\end{array}\right)$ , then:

$ker(T)=\left\{{\bf x}\in \mathbb{R}^{2}: A{\bf x}=0\right\}$ .

So, to find ker(T) you must solve the homogenous equation

$A{\bf x}=\left(\begin{array}{cc}2&1\\3&4\end{array}\right) \left(\begin{array}{c} x&y \end{array}\right)=\left(\begin{array}{c}0&0\end{array}\right)$

Using Gauss elimination we obtain the simpler equivalent system

$\left(\begin{array}{cc} -6&3\\0&5\end{array}\right) \left(\begin{array}{c} x&y\end{array}\right)=\left(\begin{array}{c}0&0\end{array}\right)$

Then, we have that

$x=0,y=0$ .

We have that $ker(T)=\{\left(\begin{array}{c}0&0\end{array}\right)\}$ . On this case we say that the basis is the empty set $\emptyset$ .

The range of $T$ is the set of vectors of the form

$\left(\begin{array}{c} \alpha &\beta\end{array}\right)=\left(\begin{array}{cc}2&1\\3&4\end{array}\right)\left(\begin{array}{c}x&y\end{array}\right)=x\left(\begin{array}{c}2&3\end{array}\right)+y\left(\begin{array}{c}1&4\end{array}\right)$

So,

$Range(T)=\langle \left(\begin{array}{c}2&3\end{array}\right), \left(\begin{array}{c}1&4\end{array}\right) \rangle.$ Where the angle brakets denotes the span.

5 0

4 years ago