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Are the following questions true or false. Please explain so I can understand. a) A system of 4 linear equations in 3 unknowns has no solutions.  b)There exist three planes in R^3 which intersect in exactly three points. c)If u, v and w are linearly dependent, then w can be written as linear combination of u and v.

Are the following questions true or false. Please explain so I can understand. a) A system of 4 linear equations in 3 unknowns has no solutions.  b)There exist three planes in R^3 which intersect in exactly three points. c)If u, v and w are linearly dependent, then w can be written as linear combination of u and v.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Are the following questions true or false. Please explain so I can understand.

a) A system of 4 linear equations in 3 unknowns has no solutions. 

b)There exist three planes in R^3 which intersect in exactly three points.

c)If u, v and w are linearly dependent, then w can be written as linear combination of u and v.

d)Let A be a 4 × 5 matrix. Then the column vectors of A are linearly dependent.

e)If u is in span{v,w} then u is in span{v+w,w−v}

f)Let A, B be two matrices. If (A − B)2 = A2 − 2AB + B2, then AB = BA.

g)If A and B are symmetric matrices, then AB is a symmetric matrix.

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