Two parts to this question **Determine if the vectors are linearly independent.**\[v_1 = \begin{bmatrix} 1 \\ -3 \end{bmatrix}, \quad v_2 = \begin{bmatrix} -2 \\ 6 \end{bmatrix}\]---**Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**- ☐ A. The vectors are linearly independent because the vector equation \( x_1v_1 + x_2v_2 = 0 \) has only the trivial solution.- ☑ B. The vectors are not linearly independent because if \( c_1 = \) [ ] and \( c_2 = 1 \), both not zero, then \( c_1v_1 + c_2v_2 = 0 \). **Determine if the columns of the matrix form a linearly independent set. Justify your answer.**---**Matrix:**\[\begin{bmatrix}-2 & -1 & 0 \\0 & -1 & 7 \\1 & 1 & -14 \\2 & 1 & -28\end{bmatrix}\]**Instructions:**Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.)- **A.** If A is the given matrix, then the augmented matrix \(\Box\) represents the equation \(Ax = 0\). The reduced echelon form of this matrix indicates that \(Ax = 0\) has more than one solution. Therefore, the columns of A do not form a linearly independent set.- **B.** If A is the given matrix, then the augmented matrix \(\Box\) represents the equation \(Ax = 0\). The reduced echelon form of this matrix indicates that \(Ax = 0\) has only the trivial solution. Therefore, the columns of A form a linearly independent set.- **C.** If A is the given matrix, then the augmented matrix \(\Box\) represents the equation \(Ax = 0\). The reduced echelon form of this matrix indicates that \(Ax = 0\) has only the trivial solution. Therefore, the columns of A do not form a linearly independent set.- **D.** If A is the given matrix, then the augmented matrix \(\Box\) represents the equation \(Ax = 0\). The reduced echelon form of this matrix indicates that \(Ax = 0\) has more than one solution. Therefore, the columns of A form a linearly independent set.

Determine if the vectors are linearly independent. V1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The vectors are linearly independent because the vector equation x, v, + x2v2 = 0 has only the trivial solution. O B. The vectors are not linearly independent because if c, =|| and c2 = 1, both not zero, then c,V, +CzV2 = 0.

Determine if the vectors are linearly independent. V1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The vectors are linearly independent because the vector equation x, v, + x2v2 = 0 has only the trivial solution. O B. The vectors are not linearly independent because if c, =|| and c2 = 1, both not zero, then c,V, +CzV2 = 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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