1)Show that the setS={[x1][x2] l x1=0} is a subspace of R^3?[x3] 1b)Show that the set T={[x1] [x2] l x1x2=x3x4} is NOT a SUBSPACE of R^4 [x3] [x4]2)Let A be an m x n matrix, where m is not equal to n....

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1)Show that the setS={[x1][x2] l x1=0} is a subspace of R^3?[x3]
1b)Show that the set T={[x1] [x2] l x1x2=x3x4} is NOT a SUBSPACE of R^4 [x3] [x4]2)Let A be an m x n matrix, where m is not equal to n. CAN the rows of A be a basis for R^n?
(SHOW proper steps to the answers)3)Use Row operations and triangular form to compute the determinant of the matrix D given below, AND determine all VALUES of p such that D is INVERTIBLE.

Answered Same DayDec 22, 2021

Answer To: 1)Show that the setS={[x1][x2] l x1=0} is a subspace of R^3?[x3] 1b)Show that the set T={[x1] [x2] l...

Robert answered on Dec 22 2021

130 Votes

1. Suppose V is an vector space and W be any subset of V . W will be
subspace if and only if a − b ∈ W for any a, b ∈ W . Using this condition
we will prove S is a subspace and T is not subspace.
(a) Let v = (0, x, y) ∈ S and w = (0, a, b) ∈ S. Then we have
v − w = (0, x− a, y − b)
Hence v − w ∈ S. This proves that S is a subspace of R3.
(b) We have
T = {(x1, x2, x3, x4) : x1x2 = x3x4}
We see that
v =...

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1)Show that the setS={[x1][x2] l x1=0} is a subspace of R^3?[x3] 1b)Show that the set T={[x1] [x2] l x1x2=x3x4} is NOT a SUBSPACE of R^4 [x3] [x4]2)Let A be an m x n matrix, where m is not equal to n....

Answer To: 1)Show that the setS={[x1][x2] l x1=0} is a subspace of R^3?[x3] 1b)Show that the set T={[x1] [x2] l...

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