1. Write = as a linear combination of the vectors V Create a matrix with these...

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1. Write = as a linear combination of the vectors V₁ Create a matrix with these columns: 2 [#] Read off the coefficients to get -1 = 3v₁ + 2v₂. 3 and V2 -H and row reduce to get 0 6:3 1 2. Determine (with justification) whether or not the following sets of vectors are linearly independent. If a set is linearly dependent, write the zero vector as a linear combination of the vectors in which not all of the coefficients are zero. (a) {0·00- Linearly dependent, because the rank of the matrix is less than the number of 0-0 (b) columns. We have NIS 1 2] in R³, given that 1 -1 3 0 (c) • {0··}-· 0 1 ›{0.00} in R³, given that 1 2 3 ~ 1 2 2 Linearly independent, because the rank equals the number of columns. +02 +1 0 in R³. 3 = 0. [1 0 5/2 0 1-1/2 00 0 Linearly dependent. As in the previous cases we can form a matrix and row reduce it - this time we get a result with rank 2. In this case you might already be able to see that there is no way to get a nonzero entry in the third column even before you start row reducing. = 0. 00 1. Write = as a linear combination of the vectors V₁ Create a matrix with these columns: 2 [#] Read off the coefficients to get -1 = 3v₁ + 2v₂. 3 and V2 -H and row reduce to get 0 6:3 1 1. Write = as a linear combination of the vectors V₁ Create a matrix with these columns: 2 [#] Read off the coefficients to get -1 = 3v₁ + 2v₂. 3 and V2 -H and row reduce to get 0 6:3 1 2. Determine (with justification) whether or not the following sets of vectors are linearly independent. If a set is linearly dependent, write the zero vector as a linear combination of the vectors in which not all of the coefficients are zero. (a) {0·00- Linearly dependent, because the rank of the matrix is less than the number of 0-0 (b) columns. We have NIS 1 2] in R³, given that 1 -1 3 0 (c) • {0··}-· 0 1 ›{0.00} in R³, given that 1 2 3 ~ 1 2 2 Linearly independent, because the rank equals the number of columns. +02 +1 0 in R³. 3 = 0. [1 0 5/2 0 1-1/2 00 0 Linearly dependent. As in the previous cases we can form a matrix and row reduce it - this time we get a result with rank 2. In this case you might already be able to see that there is no way to get a nonzero entry in the third column even before you start row reducing. = 0. 00 1. Write = as a linear combination of the vectors V₁ Create a matrix with these columns: 2 [#] Read off the coefficients to get -1 = 3v₁ + 2v₂. 3 and V2 -H and row reduce to get 0 6:3 1