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3 years ago

can someone check my answers? i'm not sure i have them all right. will fan and give a medal for help! attached below

Mathematics

1 answer:

vekshin13 years ago

8 0

I will go with yes .

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Linear function or exponential function ?

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Assume that T is a linear transformation. Find the standard matrix of T. T: R^3 right arrow R^2 , T(e 1) =(1,2), and T(e2 ) =( -

irina [24]

Answer:

$A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]$

Step-by-step explanation:

Given

$T:R^3->R^2$

$T(e_1) = (1,2)$

$T(e_2) = (-4,6)$

$T(e_3) = (2,-6)$

Required

Find the standard matrix

The standard matrix (A) is given by

$Ax = T(x)$

Where

$T(x) = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]$

$Ax = T(x)$ becomes

$Ax = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]$

The x on both sides cancel out; and, we're left with:

$A = [T(e_1)\ T(e_2)\ T(e_3)]$

Recall that:

$T(e_1) = (1,2)$

$T(e_2) = (-4,6)$

$T(e_3) = (2,-6)$

In matrix:

$(a,b)$ is represented as: $\left[\begin{array}{c}a\\b\end{array}\right]$

So:

$T(e_1) = (1,2) = \left[\begin{array}{c}1\\2\end{array}\right]$

$T(e_2) = (-4,6)=\left[\begin{array}{c}-4\\6\end{array}\right]$

$T(e_3) = (2,-6)=\left[\begin{array}{c}2\\-6\end{array}\right]$

Substitute the above expressions in $A = [T(e_1)\ T(e_2)\ T(e_3)]$

$A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]$

Hence, the standard of the matrix A is:

$A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]$

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3 years ago

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garri49 [273]

-3.3333 is the answer

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3 years ago

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frutty [35]

Answer:

Step-by-step explanation:

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