Question

Let w be a subspace of R", and let wt be the set of all vectors orthogonal to W. Show that wt is a subspace of R" using the following steps. a. Take z in wt, and let u represent any element of W. Then zu u = 0. Take any scalar c and show that cz is orthogonal to u. (Since u was an arbitrary element of W, this will show that cz is in wt.) b. Take z, and zz in wt, and let u be any element of W. Show that z7 +22 is orthogonal to u. What can you conclude about 24 +22? Why? C. Finish the proof that wt is a subspace of R" a. How can two vectors be shown to be orthogonal? O A. Determine if the dot product of the two vectors is zero. O B. Determine if the dot product of the two vectors is less than zero. O c. Determine if the dot product of the two vectors is greater than zero. Which of the following statements should be used to find cz.u? O A. (cu). V = C(u.V) O B.u.u20, and u. U = 0 if and only if u = 0 O C. U.V = Vou OD. (U+V).W=uW+V.W Because cz. u = 0, cz is orthogonal to u. b. What are the values of 21. u and 22.u? 2.u=0 22. u= 0 Which of the following statements should be used to find (27 +22) .u? OA. U.V=V.u OB. u.u20, and u.u = 0 if and only if u = 0 O c. (u + V).W= u.W+V.W

Answer 1

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