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  3. for each of (a)-(d) below, decide whether the stat

For each of (a)-(d) below, decide whether the statement is True or False. If True, explain...

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Advance Math

For each of (a)-(d) below, decide whether the statement is Trueor False. If True, explain why. If False, give acounterexample.

(a) Two non-parallel planes in R 3 will always meet in aline.

(b) Let v, x1, x2 ∈ R 3 with x1 6= x2. Define two lines L1 andL2 by

L1 : (x, y, z) = x1 + sv, s ∈ R,

L2 : (x, y, z) = x2 + tv, t ∈ R.

Then the lines L1 and L2 will never intersect.

(c) Let v1, v2, v3 be three non-zero vectors in R 3 . Then 0(the zero vector) is a linear combination of v1, v2 and v3. (d) IfA and B are two 2 × 2 matrices, and AB = 02×2 (where 02×2 is the 2× 2 zero matrix), then at least one of A or B must be the zeromatrix.

Answer & Explanation Solved by verified expert
4.0 Ratings (539 Votes)
aYes two parallel planes always meat in a line And it can beshown by linear algebra since if you consider the following systemof the two plane    See Answer
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