Question

In: Advanced Math

T/F 1) The function f(x) = x1 − x2 + ... + (−1)n+1xn is a linear...

T/F

1) The function f(x) = x1 − x2 + ... + (−1)n+1xn is a linear function, where x = (x1,...,xn).

2) The function f(x1,x2,x3,x4) = (x2,x1,x4,x3) is linear.

3) For a given matrix A and vector b, equation Ax = b always has a solution if A is wide

Expert Solution

1) If and and is scalar, then

Therefore, is linear (TRUE).

2) If and and is scalar, then

Therefore, is linear (TRUE).

3) Consider the wide matrix

and the vector

If has a solution then we get

which means

But the first equation itself implies , so that the system above can not have any solution. Thus, the statement in question is FALSE.

Colby Messinger answered 10 months ago

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