When it comes to real vector spaces, linear independence is a term that refers to a group of vectors that do not echo or replicate the content of each other. Technically speaking, if a set of vectors is deemed linearly independent, it means that not a single vector in the group can be represented as a linear combination of the remaining vectors.
| Topic | Problem | Solution |
|---|---|---|
| None | to $A$, and use $B$ to give all solutions of the … | We are given two matrices A and B, where A represents the coefficients of the variables in the syst… |
| None | Score: $9.5 / 10 \quad 9 / 10$ answered Question … | First, we find a vector that is orthogonal to both \(\vec{u} = \langle 3,4,-2 \rangle\) and \(\vec{… |
| None | Score: $9.5 / 10$ $9 / 10$ answered Progress sav … | Given vectors \(\vec{u} = \langle 3,2,-1 \rangle\) and \(\vec{v} = \langle 0,1,5 \rangle\) |
| None | If $v_{1}=(1,0,3) ; v_{2}=(0,2,4) ; v_{3}=(3, x, … | Since the vectors are linearly dependent, the determinant of the matrix formed by these vectors sho… |
| None | 6. If the set $\left\{\left[\begin{array}{c}4 \\ … | Form the matrix and calculate its determinant: $\begin{vmatrix} 4 & -2 & 3 \\ 3 & 0 & a \\ 11 & -4 … |