3. Given A= [1 0 (a) Give the vector c so that Ax = b has a solution if and only if b - c = 0. (b) Give a basis of the subspace of all vectors b such that Ax = b has a solution. %3D

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Q: §5.1, Exercise 17. For which scalars a, b, c do the solutions to the equation ax + by = c form a…

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Q: Find (a) a basis for the row space and (b) the rank of the matrix. [0  1 −2]

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Q: Construct a 3 x3 nonzero matrix A such that the vector is a solution of Ax = 0. 1 LA =

A: x=-1-1  1 Now let A=abcdefghi be the required vector. Then, Ax=0⇒abcdefghi-1-1  1=000⇒-a-b+c-d-e+f…

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A: see my solution

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Q: [1 2 2 4 6 2. Find a basis for the four subspaces of A = |1 2 3 6 9 0 0 1 2 3

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A: This question is related to Linear Algebra

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A: given  system of linear equations 2x1+x2-8x3+6x4=0   ...ix1+2x2-4x3+12x4=0   ...iix1+x2-4x3+6x4=0…

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A: The solution is given as

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A: The given matrix,

Q: Please see image

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Q: 2. Find the matrices P and D for an orthogonal diagonalization A=PDPT for 3 0 0 A=

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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.