Consider the following set of vectors. 3 ~ -[-] ~ = V 6 Let v and...

 

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Consider the following set of vectors. 3 ~ -[-] ~ = V₂ 6 Let v and v₂ be (column) vectors in R³ and let A be the 3 x 2 matrix 1 homogeneous linear system with augmented matrix [A10] has a nontrivial solution. Consider the following equation. 3 9[-1]+2₂ 6 -1 3 6 -1 3 6 = -[:] 0 1 Determine if the vectors v V1 and V₂ are linearly independent. The set of vectors is linearly dependent. The set of vectors is linearly independent. V1 V₂ are linearly dependent if and only if the and with these vectors as its columns. Then v Solve for C₁ and C2. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {C₁, C₂} = {0, 0}.) {C₁₂₁ ²₂ } = { Consider the following set of vectors. 3 ~ -[-] ~ = V₂ 6 Let v and v₂ be (column) vectors in R³ and let A be the 3 x 2 matrix 1 homogeneous linear system with augmented matrix [A10] has a nontrivial solution. Consider the following equation. 3 9[-1]+2₂ 6 -1 3 6 -1 3 6 = -[:] 0 1 Determine if the vectors v V1 and V₂ are linearly independent. The set of vectors is linearly dependent. The set of vectors is linearly independent. V1 V₂ are linearly dependent if and only if the and with these vectors as its columns. Then v Solve for C₁ and C2. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {C₁, C₂} = {0, 0}.) {C₁₂₁ ²₂ } = {