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3 years ago

Expand the expression 7(1/9a + 2)

Mathematics

1 answer:

Assoli18 [71]3 years ago

5 0

Answer: $\frac{7\left(18a+1\right)}{9a}$

Step-by-step explanation:

$7\left(\frac{1}{9a}+2\right)$

$=7\cdot \frac{2\cdot \:9a+1}{9a}$

$=7\cdot \frac{18a+1}{9a}$

$=\frac{7\left(18a+1\right)}{9a}$

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T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
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A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

$\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]$

The inverse of the matrix is

$\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]$

So, the Inverse Transformation is given by

$T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$

So, no option is correct. And the answer is

$T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$

Learn more about linear transformations here-

brainly.com/question/13005179

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