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Problem 2: For each of the matrices below, 1) find a value of k such that Nul(A) is a subspace of Rk, 2) find a nonzero vecto

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Answer #1

we have ។ 0 A= -2 0 -5 -5 7 0 -S 7 -2 Apply now operations we get -217 0 R, IR 0 -5 -2 21 -5 7 7 -2 -2/4 -411 R1 R₂ + 2R RytO 5/2 3574 0 Ryt Rythy 11 Rg 14 Rs 203 I 2 0 0 0 0 0 O R; 4 R - 50 Rz Beth 35 2 N - 0 0 0 0 0 0 0 2 muf(A)1) since number of columi un A :کلمه کیک في معممططهمشيميلسى یک = X هكليN (2 -Ax= م = 0 و 0 ره وه - 0 0 0 ہ ہ متيميوعملالبومهhen [ Alv] -2 O 5 -2 -5 o -7 0 7 2 HPL -5 ។ 0 0 6 0 1 0 0 0 1 0 0 0 This systemo has a unique solutóp. so visuin WLA). b) we0 2 0 0 -2 1) Number of then Nuta) ui a eusspace og RS 165 Fox Nulla) AX=0 1 0 O 212 O -2 2 0 23 O Hy Lii get 2 + 273 - 130_12 E Nul(AL o re & 2 Number of course ser collal is a seusabace of akz2 R² 4 VE 11 FEY Ax= v LAIV] 6 4 5 4 4 - 0 - - 0 2 - 0 2

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