Question-219697

Question Number 219697 by Spillover last updated on 01/May/25

Answered by Spillover last updated on 01/May/25

Answered by Spillover last updated on 01/May/25

2 2 3
1 5 —2
4 1 9
3 7 4

R₄ — 3R₂

2 2 3
1 5 —2
4 1 9
0 -8 10

R₃ — 4R₂

2 2 3
1 5 —2
0 -19 17
0 -8 10
R₁ — 2R₂

0 -8 7
1 5 —2
0 -19 17
0 -8 10
R₄ — R₁

0 -8 7
1 5 -2
0 -19 17
0 0 3

R₃ — ¹⁹/₈R₁

0 -8 7
1 5 -2
0 0 ³/₈
0 0 3

8R₃

0 -8 7
1 5 -2
0 0 3
0 0 3

R₄ — R₃

0 -8 7
1 5 -2
0 0 3
0 0 0

The dimension is 3, hence it spans ℝ³.