Question

4 11. (5 points) Find the row space and null space of A= 1 0 -2 1 2 1 -4 -1 -2 -8

Answer 1

Given Matrix is. 4 2 1 2. -T A Row. Space -8 - 4 - 2 Calculate 2 times row i to row 3 Add 1 4 2 1 1 Add -4 times es row 2 to row I 0 -2 - 1 0 The nonzero rows in the reduced row.echelon form are a basis for the now space! S[10,- 2,5] [0,1,1,-) (Ans.)

③ Nell space Calculate. - Criven Matrix, 4. 2 -2 - 8 -4 -2 To find a basis for the neell space, we form an argumented matrix by appending pol- this matrix in reduced row. echelon We begin with the matrix: - form. 4 2 1 - 2 L- 2-8 - 4 Add 2 times row I to row 3: 4 2 1 o 0 Add & times sow a to row 1: - 2 5 o . ово O 0 to back on convert the matrix equivalent system equation mi + 2Nz & MI SNA 12 t R3 - na Add an equation for each free variables ni - 203 sna 12 t 13 + -24 = 13 ng 1 VA 11 WA

solve for each wariable in terms of the free voriables! - 2ng & -50A 82 - 13 ra x3 13 КА Na collect terms into vectors: 203 -sna ng 12 n3 na -13 43 A Na factor out variables on on the right side: x 2 12 rez res & ka na Thus, basis for the nell space is! a 2 2 (Ane.) Z