What is the solution to the system of equation required with this matrix? [1 0 0

Question

What is the solution to the system of equation required with this matrix? [1 0 0 2 0 1 0 3 0 0 0 4] x = 2, y = 3, z = 4 x = -1, y = 1, z = 1 There are infinite number of solutions There is no solution We find that a system of three linear equations in three variables has no solutions. This means that all three planes must be parallel. at least two of the planes must be parallel. at least two of the equations represent the same plane None of the above. A vector space does not have to satisfy which of the following properties? Closure under vector addition. Closure under scalar multiplication. Closure under vector multiplication A vector subspace must satisfy all of the above properties Let A = [1 0 2 1 0 1 3 1 2 -1 1 1] Which of the following vectors is in the null space of A? [-2 0 -1] [3 3 3] [2 3 -1 0] [3 -1 3]

Explanation / Answer

1.1) d) There is no solution. as Rank of matrix and augment matrix is not same.

1.2) b) Atleast two plane must be parallel. because in this case rank of matrix and augmented matrix will not be same.

1.3) c) closure under vector multiplciation. it is not an axiom to prove a space a vector space.

1.4) c) because it should be 4x1

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