Linear Independence Worksheet with Answer Key

What's on the worksheet

1. Each list below is linearly dependent.
2. Vectors v_1, v_2, v_3 and b in some R^n satisfy both \mathbf{b} = 2\mathbf{v}_1 - \mathbf{v}_2 + 3\mathbf{v}_3 \quad \text{and} \quad \mathbf{b} =…
3. Let v_1 = (1, 2, 0, -1), v_2 = (2, 3, 1, 0), v_3 = (0, 1, -1, -2), v_4 = (0, 1, -1, 3) and v_5 = (3, 4, 2, -4) in R^4.
4. Show by row reduction that v_1 = (1, -2, -3, 1, -3), v_2 = (1, 0, 1, 3, 3) and v_3 = (6, -4, -2, 14, 6) in R^5 are linearly dependent.
5. Let v_1, , v_k be a linearly independent list in R^n, and let w be a vector of R^n that is not a linear combination of v_1, , v_k.