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Unformatted text preview: CHAPTER 4 MATLAB EXERCISES 4–1 CHAPTER 4 ❑ MATLAB EXERCISES 1. Let and Use MATLAB to write (if possi- ble) the vector v as a linear combination of the vectors and (a) (b) 2. Use MATLAB to determine whether the given set of vectors spans (a) (b) 3. Use MATLAB to determine whether the set is linearly independent or dependent. (a) (b) 4. Use MATLAB to determine whether the set of vectors forms a basis of (a) (b) (c) (d) 5. Suppose you want to find a basis for that contains the vectors and One way to do this is to consider the set of vectors consisting of and together with the standard basis vectors, and Let A be the matrix whose columns consist of the vectors and , and apply rref to A to obtain Since the leading ones of the reduced matrix on the right are in columns 1, 2, 3, and 6, a basis for consists of the corresponding column vectors of A convenient way to construct the matrix A is to define the matrix B whose columns are the given vectors and Then A is simply the matrix obtained by adjoining the identity matrix to Use this algorithm to find a basis for...
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