Need help with some linear algebra questions

In summary, the conversation discussed the speaker's family situation where their mom was unable to work due to illness and the speaker had to work two jobs while being a full-time student to help with the mortgage payments. As a result, they may need to temporarily pause their studies in 2015 to support their family until their mom recovers. The speaker also mentioned having an exam on Monday and requesting help with some questions they were unsure about, providing screenshots of the questions. The responder reminded the speaker of the forum rules and advised them to post each question separately in the appropriate homework forum with the relevant definitions and their attempt at solving the problem, as they are not allowed to give complete answers but can provide hints. They also suggested posting earlier for quicker
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KevinCT
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Okay, long story short, my mom could not work because of an illness so me and and family all had to chip in so fulfill the mortgage payment on our home. I worked two jobs and am a full-time student. I've been studying as much as I possibly can and may have to temporarily restrain from spring classes on 2015 due to needing to provide for my family until my mom recovers. I have an exam on Monday and could use some help on some questions in which I am not sure how to go about. Tried reading the textbook but it wasn't helpful.

http://speedcap.net/sharing/files/fb/bb/fbbbf32c7f1150653d7ecdc2fcaa12dd.png
http://speedcap.net/sharing/files/d0/e3/d0e3963b9802ef2300a124f2eb0f689d.png http://speedcap.net/sharing/files/d3/8e/d38e2092f1abdee19642a20cc2354307.png http://speedcap.net/sharing/files/33/ca/33cae85323f2d83fba38882956ea1833.png http://speedcap.net/sharing/files/07/ef/07ef2ce098daa6b536a1a729c0534f9c.png http://speedcap.net/sharing/files/60/38/60385f0cf9c61b07aeaa9c17fe103a63.png

There are 22 questions but these 6 were ones I could not get to solve. Thanks. Would be helpful if you showed it in detail as well.
 
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  • #2
Welcome to Physics Forums. The rules at this site require us to treat all textbook-style problems as homework. You should start one thread for each problem, in the appropriate homework forum. (In this case, that would be the "calculus & beyond" homework forum). You have to use the template when you start the threads, and you have to show us your work up to the point where you're stuck. If you "don't know where to begin", you at least have to post the relevant definitions and an attempt to use them. We are not allowed to give you complete answers. We can only give you hints.

As I'm sure you have already realized, you should have come here at least a couple of days earlier. But there's still a good chance that you will get good answers to all your questions quickly, if you do your part. (Don't put URGENT in the titles or anything like that. The only thing you can do to get faster answers is to make sure that you're providing all the information the helpers need).
 
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1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of linear equations and their representations in vector spaces. It involves solving systems of linear equations, manipulating matrices, and understanding geometric transformations.

2. Why is linear algebra important?

Linear algebra is a fundamental tool in many fields, including physics, engineering, computer science, and economics. It provides a powerful framework for solving complex problems involving linear relationships and is essential for understanding higher-level mathematical concepts.

3. What are some common applications of linear algebra?

Linear algebra has numerous applications, including image and signal processing, data compression, machine learning, quantum mechanics, and computer graphics. It is also used in solving optimization problems, calculating probabilities, and analyzing networks.

4. What are the basic concepts in linear algebra?

Some of the basic concepts in linear algebra include vector spaces, linear transformations, matrices, determinants, eigenvalues, and eigenvectors. These concepts are used to represent and solve systems of linear equations, perform operations on vectors and matrices, and analyze geometric transformations.

5. How can I improve my understanding of linear algebra?

To improve your understanding of linear algebra, it is essential to practice solving problems and working with matrices and vectors. You can also read textbooks, watch online tutorials, or attend lectures to gain a deeper understanding of the concepts. Additionally, working on real-world applications can help solidify your understanding of linear algebra.

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