Consider two linear transformations y = T(x) and z = L(y), where T goes from R^m to R^p and L goes from R^p to R^n. Is the transformationz = L(T(x)) linear as well ? [The transformation z = L(T(x)) is called the composite of T and L.]

Answers

Answer 1

Answer: Yes.

Proof: Consider x, y in R^m. Then since T is linear, we have:

T(a*x + b*y) = a*T(x) + b*T(y)

But since L is linear, we have:

L(a*T(x) + b*T(y)) = a*L(T(x)) + b*L(T(y))

So:

L(T(a*x + b*y)) = a*L(T(x)) + b*L(T(y))

and the composition is linear.

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Which system of equations can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x?

Answers

we have

$4x^5-12x^4+6x=5x^3-2x$

Separate the equation above in two equations

equation $1$

$y=4x^5-12x^4+6x$

equation $2$

$y=5x^3-2x$

we know that

In a system of equations the roots of the equation $1$ must satisfy equation $2$ and the roots of the equation $2$ must satisfy equation $1$

therefore

the answer is

The system of equations is

$y=4x^5-12x^4+6x$

$y=5x^3-2x$

Simplifying 4x4 = 12x2 Solving 4x4 = 12x2 Solving for variable 'x'. Reorder the terms: -12x2 + 4x4 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -12x2 + 4x4 = 0 Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(-3 + x2) = 0

Use the Distributive Property to evaluate each expression.-2(8-5)

A. -21
B. -6
C. 6
D. 18

Answers

Answer: c

Step-by-step explanation:

You multiply each number by 2 and then you subtract each number then you finally get 6

3m - 3(m+8) > 3m(Teacher didn't go over this hopefully I can get an explanation)

Answers

Alrighty!

*Note the ">" sign is similar to the "=" sign.

3m - 3(3m + 8) > 3m
3m - 6m + 24 > 3m (distribute)
-3m + 24 > 3m (combine like terms)
24 > 6m (Compute/simplify)
8 > m

Makes sense?

Sinhx = 8/15 what are the other hyperbolic functions?

Answers

cosh^2x - sinh^2x = 1

coshx = sqrt( 1 + sinh^2x)

= sqrt(1 + (8/15)^2) = 17/15

for tanh

just divide

sinhx/coshx = tanhx = 8/17

for sech , cosech, coth << just flip the original as normal trigonometric functions

Evaluate the floor function f(x) = ⌊x⌋ for the given input values. f(2) = f(6.8) = f(–3.3) =

Answers

Answer:

f(2) = 2 , f(6.8) = 6 and f(-3.3) = -4.

Step-by-step explanation:

We are given,

Floor function is $f(x)=\left \lfloor x \right \rfloor$ .

That is, the function have value,

$f(x)=n$ when $n\leq x< n+1$ .

So, we get,

For $2\leq x< 3$ , we have f(2) = 2

For $6\leq x< 7$ , we have f(6.8) = 6

For $-4\leq x< -3$ , we have f(-3.3) = -4

Thus, we have the values,

f(2) = 2 , f(6.8) = 6 and f(-3.3) = -4.

Answer:

The correct answers on edge .. yw have a great dayy

Step-by-step explanation:

f(2) =

f(6.8) =

f(–3.3) =

-4

Tom conducted a drawing competition at school. He bought 5 boxes of colored pencils and spent $5.25 on drawing paper. However, more contestants entered than he expected, and he had to buy 2 more boxes of colored pencils. The total cost of the paper and pencils was $82.95. Identify the equation and solution that would help to find the cost of each box of pencils.

Answers

82.92 - 5.25 = 77.67
77.67 divided by 8 =
$9.70 per box

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