# Can anyone explain why (linear algebra)

• frasifrasi
In summary, the union of subspaces V and W in R^n is not always a subspace of R^n. This can be seen through examples such as the union of two lines through the origin in R^2. Even if v is in subspace V and w is in subspace W, it is not guaranteed that v+w will be in V\cupW. A specific counterexample can be given using Vid's suggestion, where V= {(x,y)| y= x}, v= (1, 1), W= {(x,y)|y= -x}, and w= (-1, 1). In this case, v+w is not in the union of V and W.
frasifrasi
Why for the subspaces V and W in R^n , the

union of V and W is not a subspace of R^n?

Thank you.

Look at some examples to see why such as the union of two lines through the origin in R^2.

If v is in subspace V and w is in subspace W, it is not, in general, true that v+ w is in V$\cup$W. You can give a specific counter example by using Vid's suggestion. Let V= {(x,y)| y= x}, v= (1, 1), W= {(x,y)|y= -x}, w= (-1, 1). Is v+ w in the union of V and W?

## 1. Can anyone explain why linear algebra is important in science?

Linear algebra is a branch of mathematics that deals with linear equations and their representations in vector spaces. It is used extensively in scientific fields such as physics, engineering, computer science, and data analysis. Linear algebra enables scientists to model complex systems and solve problems that involve multiple variables and equations, making it an essential tool for understanding the world around us.

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Linear algebra has numerous real-world applications in fields such as physics, engineering, economics, and data science. It is used to solve complex optimization problems, model systems, analyze data, and make predictions. For example, in economics, linear algebra is used to analyze supply and demand curves and make predictions about market trends. In physics, it is used to study quantum mechanics and describe the behavior of particles.

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