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B) Prof brilliant SWachs inhis class- He introduces the concent Vco SC"(7 nt anens Ard XSSIl As A eXetrise he gives Wacol GDaCT of dimension #ik and z find thie basis batsed 0n the following: should stat with which has single HOD-ZCTO element of and build the bxasis by addling vectors such that 5 linearly inclependlent . The precess shonkl bee stopped once eleme Hts eced StaltL with which hats mOrC Ual elcucuts Vn k > FuT clemcnl such Unt ccomns linearly independent . The Next day bntg t
b) Prof brilliant SWachs inhis class- He introduces the concent Vco SC"(7 nt anens Ard XSSIl As A eXetrise he gives Wacol GDaCT of dimension #ik and z find thie basis batsed 0n the following: should stat with which has single HOD-ZCTO element of and build the bxasis by addling vectors such that 5 linearly inclependlent . The precess shonkl bee stopped once eleme Hts eced StaltL with which hats mOrC Ual elcucuts Vn k > FuT clemcnl such Unt ccomns linearly independent . The Next day bntg their working; Prol: #skshe CSt working d 2 ,the Ghmi Sels While student SaVe student W Siln hed mOL MU Ftol: says that both ad W could be correct. Justify the statement of Prof. X with suitable examples of V, aId T.
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Explain why the following form linearly dependent sets of vectors. (Solve this problem by inspection.) (a) $\mathbf{u}_{1}=(-1,2,4)$ and $\mathbf{u}_{2}=(5,-10,-20)$ in $R^{3}$ (b) $\mathbf{u}_{1}=(3,-1), \mathbf{u}_{2}=(4,5), \mathbf{u}_{3}=(-4,7)$ in $R^{2}$ (c) $\mathbf{p}_{1}=3-2 x+x^{2}$ and $\mathbf{p}_{2}=6-4 x+2 x^{2}$ in $P_{2}$ (d) $A=\left[\begin{array}{rr}-3 & 4 \\ 2 & 0\end{array}\right]$ and $B=\left[\begin{array}{rr}3 & -4 \\ -2 & 0\end{array}\right]$ in $M_{22}$
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