Math  /  Algebra

QuestionLet A=[220211321]A=\left[\begin{array}{ccc} -2 & 2 & 0 \\ 2 & -1 & 1 \\ 3 & -2 & 1 \end{array}\right] a. A basis for the row space of AA is {}\{\square\}. You should be able to explain and justify your answer. Enter a coordinate vector, such as 1,2,3>\langle 1,2,3>, or a comma separated list of coordinate vectors, such as 1,2,3,4,5,6\langle 1,2,3\rangle,\langle 4,5,6\rangle. b. The dimension of the row space of AA is \square because (select all correct answers -- there may be more than one correct answer): A. rref(A)\operatorname{rref}(A) is the identity matrix. B. Two of the three rows in rref(A)\operatorname{rref}(A) have pivots. C. The basis we found for the row space of AA has two vectors. D. Two of the three columns in rref(A)\operatorname{rref}(A) are free variable columns. E. rref(A)\operatorname{rref}(A) has a pivot in every row. F. Two of the threê rows in rref(A)\operatorname{rref}(A) do not have a pivot. c. The row space of AA is a subspace of \square because choose \square d. The geometry of the row space of AA is choose \square

Studdy Solution
a. A basis for the row space of AA is 2,2,0,2,1,1\langle -2, 2, 0 \rangle, \langle 2, -1, 1 \rangle. b. The dimension of the row space of AA is **2** because B and C are correct. c. The row space of AA is a subspace of R3\mathbb{R}^3. d. The geometry of the row space of AA is a plane.

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