Find the measure of

With bases V1, V2 , V3 andw1, w2 , W3, suppose T(v1) = w2 and T(v2) = T(v3) = w1 + w3 . T is a linear transformation. Find the m

Roman55 [17]

Answer:

See picture and explanation below.

Step-by-step explanation:

With this information, the matrix A that you can find is the transformation matrix of T. The matrix A is useful because T(x)=Av for all v in the domain of T.

A is defined as $T=([T(v_1)] [T(v_2] [T(v_3)])\text{ where }[T(v_i)]$ denotes the vector of coordinates of $T(v_i)$ respect to the basis (we can apply this definition because forms a basis for the domain of T).

The vector of coordinates can be computed in the following way: if $T(v_i)=a_1w_1+a_2w_2+a_3w_3$ then $[T(v_i)]=(a_1,a_2,a_3)^t$ .

Note that we have all the required information: $T(v_1)=0w_1+1\cdot w_2+0w_3$ then $[T(v_1)]=(0,1,0)^t$

$T(v_2)=T(v_3)=1\cdot w_1+0w_2+0w_3$ hence $[T(v_2)]=[T(v_3)]=(1,0,0)^t$

The matrix A is on the picture attached, with the multiplication A(1,1,1).

Finally, to obtain the output required at the end, use the properties of a linear transformation and the outputs given:

$T(v_1+v_2+v_3)=T(v_1)+T(v_2)+T(v_3)=w_2+w_1+w_1=w_2+2w_1$

In this last case, we can either use the linearity of T or multiply by A.

4 0

3 years ago

Need help in this mathquestion. The function h(x)=(x+2)^2 can be expressed in the form f(g(x)) where f(x)=x^2 , and g(x) is defi

blsea [12.9K]

Answer:

In a nutshell, $g(x) = x+2$ .

Step-by-step explanation:

A composition is operation between function that consist in replacing the independent variable of the first function, $f(x)$ in this case, for $g(x)$ . Common notations for composition between functions are $f(g(x))$ and $f\circ g (x)$ . If we know that $h(x) = f\circ g (x) = (x+2)^{2}$ and $f(x) = x^{2}$ , then $g(x) = x+2$ .

In a nutshell, $g(x) = x+2$ .

4 0

3 years ago

Explain how to multiply square roots

Dmitry_Shevchenko [17]

Answer:

To multiply square roots, first multiply the radicands, or the numbers underneath the radical sign. If there are any coefficients in front of the radical sign, multiply them together as well. Finally, if the new radicand can be divided out by a perfect square, factor out this perfect square and simplify it.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The sum of -7.68 and it’s additive inverse is??

Readme [11.4K]

The answer is 0. the additive inverse of a negative number is the same number but positive. to find the sum means to add them together. for example take 2 and -2. 2 is the additive inverse of -2. if you add 2+-2 the answer comes out to 0

4 0

3 years ago

A cyclist estimates that he will bike 80 miles this week. He actually bikes 75.5 miles. What is the percent error of the cyclist

maw [93]

Answer:

<em>The percent error of the cyclist's estimate is 5.63%</em>

Step-by-step explanation:

<u>Percentages</u>

The cyclist estimates he will bike 80 miles this week, but he really bikes 75.5 miles.

The error of his estimate in miles can be calculated as the difference between his estimate and the real outcome:

Error = 80 miles - 75.5 miles = 4.5 miles

To calculate the error as a percent, we divide that quantity by the original estimate and multiply by 100%:

Error% = 4.5 / 80 * 100 = 5.625%

Rounding to the nearest hundredth:

The percent error of the cyclist's estimate is 5.63%

5 0

2 years ago