Project using simple formulas

What would you have to know about the pivot columns in an augmented matrix in order to know that the linear system is consistent

Scrat [10]

Answer:

The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.

$rank(A)=rank\left ( \left [ A|B \right ] \right )\:and\:n=rank(A)$

Then satisfying this theorem the system is consistent and has one single solution.

Explanation:

1) To answer that, you should have to know The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.

$rank(A)=rank\left ( \left [ A|B \right ] \right )\:and\:n=rank(A)$

$rank(A)$

Then the system is consistent and has a unique solution.

$\left\{\begin{matrix}x-3y-2z=6 \\ 2x-4y-3z=8 \\ -3x+6y+8z=-5 \end{matrix}\right.$

2) Writing it as Linear system

$A=\begin{pmatrix}1 & -3 &-2 \\ 2& -4 &-3 \\ -3 &6 &8 \end{pmatrix}$ $B=\begin{pmatrix}6\\ 8\\ 5\end{pmatrix}$

$rank(A) =\left(\begin{matrix}7 & 0 & 0 \\0 & 7 & 0 \\0 & 0 & 7\end{matrix}\right)=3$

3) The Rank (A) is 3 found through Gauss elimination

$(A|B)=\begin{pmatrix}1 & -3 &-2 &6 \\ 2& -4 &-3 &8 \\ -3&6 &8 &-5 \end{pmatrix}$

$rank(A|B)=\left(\begin{matrix}1 & -3 & -2 \\0 & 2 & 1 \\0 & 0 & \frac{7}{2}\end{matrix}\right)=3$

4) The rank of (A|B) is also equal to 3, found through Gauss elimination:

So this linear system is consistent and has a unique solution.

8 0

3 years ago

Which one of the following words is NOT an action verb?

pochemuha

Pretty sure the answer is D.Happy

3 0

4 years ago

Read 2 more answers

Non-delivered goods, counterfeit products, fraudulent payments are common type of cyber crime these

Arisa [49]

Answer:

a. Internet auction fraud

b. Counterfeit products are products made and/or sold under the brand name of a product of a higher quality

c. 1) Monitor business transactions

2) Use an Address Verification System AVS

Explanation:

a. Such types of cyber crimes are collectively called Internet auction fraud

Internet or online auction fraud is a form of fraud that involves the act of providing misleading information about goods paced on advert for sale on an online auction site, including the sale of counterfeit goods, sale of goods of poor quality, receiving a different item from what was ordered, artificial bidding to increase price, omission of important information about a product, delivering an item that looks different from what was displayed on the website and the non-delivery of an item already to the buyer.

A seller can be a victim of the internet auction fraud when a buyer does not pay for goods an/or services received, request for delivery before payment, the buyer pays with a stolen credit card, the buyer uses a fake escrow account such that the money returns to the buyer after receiving the goods

b. Counterfeit products or goods are products that are being manufactured and marketed, without formal authorization, under the name of a popular and recognized but are usually of lesser quality than the product they try to imitate

c. Measures that can be taken to stop fraudulent payments are;

1) Monitor transactions to to check for red flags, including disparity in shipping and billing information

Monitor transactions from customer that use free or anonymous emails services which can easily be opened and closed without payment or proper documentation

2) Make use of Address Verification System to authenticate the billing address on a payment, and the address on the credit card.

7 0

3 years ago

.A card that connects directly to the motherboard of the computer and has external sockets so that the computer can be connected

mylen [45]

Answer: Network interface controller

Explanation:

A network interface controller is also referred to as the network adapter or LAN adapter. It is simply a component of the computer hardware that is used to connects a computer system to a particular network.

It is a card that connects directly to the motherboard of the computer and has external sockets so that the computer can be connected to a network via cables.

6 0

3 years ago

Technician A says that a cracked exhaust manifold can affect oxygen sensor operation. Technician B says that a clogged air filte

liraira [26]

Answer:

tech A only

Explanation:

Technician A is right because a cracked exhaust manifold allows more oxygen into the exhaust stream, which affects oxygen sensor voltage. Technician B is wrong because a clogged air filter raises Hydrocarbons (HC) and also affects O2 (Oxygen) and CO (Carbon Monoxide) levels.

8 0

3 years ago