Math  /  Algebra

Questionاجتماع لترشيج لنادي الشطرنج Forms - Google Drive Google Translate Translate Micrometer Instructional Techno... ChatGPT C.E 123 مكهبة - Goo.. Dashboard | Pre (b) 1 (c) 2 (d) 3. (11) Which of the following is a subspace of P3P_{3} ? (a) S={pP3:p(1)=1}×S=\left\{p \in P_{3}: p(1)=1\right\} \times ax2+bx+ca x^{2}+b x+c (b) S={pP3:p(1)=0}S=\left\{p \in P_{3}: p(1)=0\right\} a+b+ca+b+c (c) β={pP3:p(0)=1}×\beta=\left\{p \in P_{3}: p(0)=1\right\} \times (少) S={pP3:p(x)=x2+ax+b,a,bR}S=\left\{p \in P_{3}: p(x)=x^{2}+a x+b, a, b \in \mathbb{R}\right\} (12) If the reduced row echelon form of AA is [122000]\left[\begin{array}{lll}1 & 2 & 2 \\ 0 & 0 & 0\end{array}\right] and a2=(2,2)Ta_{2}=(2,2)^{T}, (a) [122121]\left[\begin{array}{lll}1 & 2 & 2 \\ 1 & 2 & 1\end{array}\right] (b) [122020]\left[\begin{array}{lll}1 & 2 & 2 \\ 0 & 2 & 0\end{array}\right] 244241\begin{array}{lll} 2 & 4 & 4 \\ 2 & 4 & 1 \end{array} (c) [122122]\left[\begin{array}{lll}1 & 2 & 2 \\ 1 & 2 & 2\end{array}\right] (d) [422422]\left[\begin{array}{lll}4 & 2 & 2 \\ 4 & 2 & 2\end{array}\right]. Search

Studdy Solution
The subspaces of P3P_3 are the set in option (b).
The matrix AA is the one shown in option (b) of the second question.

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