Eliza T.

True or False Linear Systems

Determine which of the following statements are true and which are false.

(a) The equation 4x − sin(1)y + 2z = 3√5 is linear.

(b) The equation xy + 4z = 4 is linear.

(c) If a system of linear equations has fewer equations than variables, then it must have infinitely many solutions.

(d) If a system of linear equations has fewer equations than variables, then it cannot have a unique solution.

(e) The vector (2, 3, 1) is a linear combination of the vectors (1, 1, 1) and (0, 1, −1).

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Mathematics Tutor

Eliza T.

(a) would be true because it's in the form whereas (b) would be false because it isn't. (c) is false because if I write in this form: [ 1 1 1 | 1 ] [ 1 1 1 | 2 ] Then subtract row 1 from row 2: [ 1 1 1 | 1 ] [ 0 0 0 | 1 ] But 0 can't equal one, therefore false. (d) would be true according to your example, because there infinitely many possibilities, as x can be 3 and y can be -2, x can also be 0 and y can also be 1 and so on. (e) would be true Thanks for the help so far!
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03/02/20

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