RIJEÃ…Â ENI ZADACI IZ MATEMATIKE

33. Da li vektori A 1 , A 2 , A 3 i A 4 čine bazu od R 4 ako su⎡ ⎤ ⎡1A 1 = ⎢1⎥⎣1⎦ , A 2 = ⎢⎣111−1−1⎤ ⎡ ⎤ ⎡ ⎤11⎥⎦ , A 3 = ⎢−1⎥⎣ 1 ⎦ iA 4 = ⎢−1⎥⎣−1⎦−1 1Rješenje:1 1 1 11 1 1 11 1 −1 −11 −1 1 −1=0 0 −2 −20 −2 0 −2=∣1 −1 −1 1 ∣ ∣0 −2 −2 0 ∣0 −2 −2= 1 · (−1) 2 ·−2 0 −2∣−2 −2 0 ∣ = 0 1 1(−2)3 ·1 0 1∣1 1 0∣ =0 1 1= −8 ·1 0 1∣1 0 −1∣ = −8 · 1 · (−1)3 ·∣ 1 11 −1∣ == 8 · (1 · (−1) − 1 · 1) = 8 · (−2) = −16 ≠ 0A 1 , A 2 , A 3 i A 4 jesu baza od R 4 .35