Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b, c, d) R4| a - b + 2c + 3d=0, -a +b - 2c - 3d=0};   U3= {a, b, c, d) R4| 1a – 2b – 1c - d=0, a + 2b + 0c + 2 d=0 };   Sub-Task 1. Find a basis and the dimension of U1.  Sub-Task 2. Find a basis and the dimension of U2.  Sub-Task 3. Find a basis and the dimension of U3.  Sub-Task 4. Whether R4=U1+U2, (provide a justification). Whether R4=U1 U2, (provide a justification). Sub-Task 5. Whether R4=U1+U3, (provide a justification). Whether R4=U1 U3, (provide a justification).   Sub-Task 6. Whether R4=U2+U3, (provide a justification). Whether R4=U2 U3, (provide a justification).

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Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

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Q: Determine all subspaces of W.

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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.