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mestny [16]
3 years ago
14

Subtract the polynomials (7.8x - 3.4y + z) and (-9.2x + 4.8y - 2.1z), then place the answer in the proper location on the grid.

Write answer in x-y-z order and include the tenths place.
Mathematics
2 answers:
Naya [18.7K]3 years ago
6 0
Subtracting the polynomials will give us:
(7.8x-3.4y+z)-(-9.2x+4.8y-2.1z)
=(7.8x+9.2x)+(-3.4y-4.8y)+(z+2.1z)
=17x-8.2y+3.1z

Answer: 17x-8.2y+3.1z
wolverine [178]3 years ago
3 0

Answer:

17.0x-8.2y+3.1z

Step-by-step explanation:

We are given that two polynomials

(7.8x-3.4y+z) and (-9.2x+4.8y-2.1z)[/tex]

We have to subtract the polynomials.

(7.8x-3.4y+z)-(-9.2x+4.8xy-2.1z)

Open the bracket

7.8x-3.4y+z+9.2x-4.8y+2.1z

Rearrange the terms

(7.8x+9.2x)-(3.4y+4.8y)+(z+2.1z)

Combine like terms

17.0x-8.2y+3.1z

Hence, the answer is given  by

17.0x-8.2y+3.1z

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Linear Algebra question! Please help!
kozerog [31]

Answers:

  1. false
  2. false
  3. true
  4. false
  5. True

==================================================

Explanation:

Problem 1

This is false because the A and B should swap places. It should be (AB)^{-1} = B^{-1}A^{-1}.

The short proof is to multiply AB with its inverse (AB)^{-1}  and we get: (AB)*(AB)^{-1} = (AB)*(B^{-1}A^{-1}) = A(B*B^{-1})*A^{-1} = A*A^{-1} = I

The fact we get the identity matrix proves that we have the proper order at this point. The swap happens so that B matches up its corresponding inverse B^{-1} and the two cancel each other out.

Keep in mind matrix multiplication is <u>not</u> commutative. So AB is not the same as BA.

-------------------------

Problem 2

This statement is true if and only if AB = BA

(A+B)^2 = (A+B)(A+B)

(A+B)^2 = A(A+B) + B(A+B)

(A+B)^2 = A^2 + AB + BA + B^2

(A+B)^2 = A^2 + 2AB + B^2 ... only works if AB = BA

However, in most general settings, matrix multiplication is <u>not</u> commutative. The order is important when multiplying most two matrices. Only for special circumstances is when AB = BA going to happen. In general,  AB = BA is false which is why statement two breaks down and is false in general.

-------------------------

Problem 3

This statement is true.

If A and B are invertible, then so is AB.

This is because both A^{-1} and B^{-1} are known to exist (otherwise A and B wouldn't be invertible) and we can use the rule mentioned in problem 1. Make sure to swap the terms of course.

Or you can use a determinant argument to prove the claim

det(A*B) = det(A)*det(B)

Since A and B are invertible, their determinants det(A) and det(B) are nonzero which makes the right hand side nonzero. Therefore det(A*B) is nonzero and AB has an inverse.

So if we have two invertible matrices, then their product is also invertible. This idea can be scaled up to include things like A^4*B^3 being also invertible.

If you wanted, you can carefully go through it like this:

  1. If A and B are invertible, then so is AB
  2. If A and AB are invertible, then so is A*AB = A^2B
  3. If A and A^2B are invertible, then so is A*A^2B = A^3B

and so on until you build up to A^4*B^3. Therefore, we can conclude that A^m*B^n is also invertible. Be careful about the order of multiplying the matrices. Something like A*AB is different from AB*A, the first of which is useful while the second is not.

So this is why statement 3 is true.

-------------------------

Problem 4

This is false. Possibly a quick counter-example is to consider these two matrices

A = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}

both of which are invertible since their determinant is nonzero (recall the determinant of a diagonal matrix is simply the product along the diagonal entries). So it's not too hard to show that the determinant of each is 1, and each matrix shown is invertible.

However, adding those two mentioned matrices gets us the 2x2 zero matrix, which is a matrix of nothing but zeros. Clearly the zero matrix has determinant zero and is therefore not invertible.

There are some cases when A+B may be invertible, but it's not true in general.

-------------------------

Problem 5

This is true because each A pairs up with an A^{-1} to cancel out (similar what happened with problem 1). For more info, check out the concept of diagonalization.

5 0
2 years ago
Please i need help urgently!!!
gladu [14]

Answer:

I'm pretty sure that it's just the negatives of the coordinates, (-3,-4) (-3,-1) (-5,-1). I don't know for sure tho, sorry if its wrong.

Step-by-step explanation:

6 0
2 years ago
To Mark or decided to purchase a new DVD player on an installment loan DVD player was $295 Tim agreed to pay $31 per month for 1
Verizon [17]

Answer: ⇒ The finance charge = $77


Step-by-step explanation:

Given: The cost price of DVD player= $295

Since, Tim agreed to pay $31 per month for 12 months .

Therefore, the total amount paid by Tim= 31\times12=\$372

The finance charge =\text{Amount paid by Tim - Cost price of DVD}

⇒ The finance charge =\$372-\ $295

⇒ The finance charge =$77

5 0
3 years ago
Pls help!! Find the volume of the flower vase. Round to the nearest tenth.
Contact [7]

Answer:

Volume = 1596.2 cubic cm

Step-by-step explanation:

Volume = volume of box - volume of cylinder

Volume = (LxWxH) - 1/3 (pi * r^2 *h)

Volume = (10 x 12 x 20) -1/3 (3.14 x 8^2 x 12)

Volume = 2400 - 803.8

Volume = 1596.2 cm^3

3 0
3 years ago
-6.25x&gt;-38 3/4<br> solve the inequality
Nostrana [21]

Answer:

Step-by-step explanation:

-6.25x > -38 3/4

-6.25x > -155/4

Multiply by (-4)

25x > 155

divide by 25,

x > 155/25

x > 31/5

x > 6.2

8 0
3 years ago
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