![Consider the following set of vectors.<br>v, =<br>3<br>, V2<br>8<br>,V3 =<br>=<br>4<br>Let v,, V2'<br>and v3<br>be (column) vectors in R³ and let A be the 3 x 3 matrix<br>v, v.<br>with these vectors as its columns. Then v.<br>v.<br>14<br>and v, are linearly dependent if and only if the<br>1<br>2'<br>homogeneous linear system with augmented matrix [A|0] has a nontrivial solution.<br>Consider the following equation.<br>7<br>C 3<br>+ c 8<br>+ C3<br>%3D<br>4<br>Solve for c,, c,, 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<br>{Cq, C2, C3} = {0, 0, 0}.)<br>{G;, Gy, Cg} = { -5 t, 1, 0<br>Determine if the vectors v,, v,, and v, are linearly independent.<br>3<br>O The set of vectors is linearly dependent.<br>O The set of vectors is linearly independent.<br>Need Help?<br>Read It<br>9:14 DM<br>](https://s3.us-east-1.amazonaws.com/storage.unifolks.com/qimg-008/008_xj0-cchthonm.png)
Extracted text: Consider the following set of vectors. v, = 3 , V2 8 ,V3 = = 4 Let v,, V2' and v3 be (column) vectors in R³ and let A be the 3 x 3 matrix v, v. with these vectors as its columns. Then v. v. 14 and v, are linearly dependent if and only if the 1 2' homogeneous linear system with augmented matrix [A|0] has a nontrivial solution. Consider the following equation. 7 C 3 + c 8 + C3 %3D 4 Solve for c,, c,, 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 {Cq, C2, C3} = {0, 0, 0}.) {G;, Gy, Cg} = { -5 t, 1, 0 Determine if the vectors v,, v,, and v, are linearly independent. 3 O The set of vectors is linearly dependent. O The set of vectors is linearly independent. Need Help? Read It 9:14 DM