Suppose we have the vectors 3 1 2 and 5 0 1 Which of the fol

Suppose we have the vectors [3 1 2] and [5 0 1] Which of the following is true? Every vector in R^3 can be written as a linear combination of the vector Some, but not all, vectors in R^3 can be written as a linear combination of these vectors. Every vector in R^3 can be written as a linear combination of the vectors More than one of the above is true. Let z be any vector from R^3. If we have a set V of unknown vectors from R^3 how many vectors must be, n V to guarantee that z can be written as a linear combination of the vectors in V? 2 3 4 It is not possible to make such a guarantee. To determine whether a set of n vectors from R^n is independent, we can form a A whose columns are the vectors in the set and then put that matrix in reduced echelon form. If the vectors are linearly independent what will we see in the diced row echelon form? A row of all zeroes. A row that has all zeros except in the last position. A column of all zeroes.) An identity matrix. Suppose a 4 times 4 matrix A has rank 4. How many solutions does the system Ax = b 0 I Infinite Not enough information is given.

Solution

1.5

Ans - B

eg - [8    0    3] can\'t be written as alinear combination of these vectors

1.6

Ans - D

The vectors of V can be multiples of one another and if z isn\'t a multiple of those vectors, then it can\'t be written as a linear combination of vectors from V.