Suppose W,, W2,. (a) span (W, W2 (b) If S; spans W; for i = 1,...,r, then S, US, U...US, spans W, + W2 + .+ W,. W, are subspaces of a vctor space V. Show that ,..., W,) = W, + W2 +..+W,.

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d)  are subspaces .

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A: See the detailed solution below.

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A: The solution is given as

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Q: Given that = 2 = -------- y = V3 = 3 10 and h -12]

A: As per the guideline, I am supposed to solve only first question from the given problems.

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Q: II. Decide which of the following are subspaces of corresponding vector spaces: C R?

A: Vector space.

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A: The solution is given in the next step.

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A: Solution of the problem as follows

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.