Linearly dependent and linearly independent vectors examples:Example 1. Check whether the vectors a = {3; 4; 5}, b = {-3; 0; 5}, c = {4; 4; 4}, d = {3; 4; 0} are linearly independent. Solution: The vectors are linearly dependent, since the dimension of the vectors smaller...
Determining value of r that makes the matrix linearly dependent for problem (a), all real numbers of value r will make the system linearly independent, as the system contains more vectors than entry simply by insepection. As for problem (b), no value of r can make the system linearly ...
The equations for nodes A, B, and C are linearly independent because each subsequent equation has a variable that the previous ones do not contain. However, the equation at node D is linearly dependent. Indeed, if we sum up the first three equations and multiply the resulting sum by −1...
Linearly Dependent Vectors:Vectors are measurements that consider the value and direction. This means that vectors would have values for each component for the direction of a measurement. Considering different vectors, we can come across vectors that are linearly dependent with each other....
The differentiation of z i with respect to time (zdot i) leads to equations which are linearly dependent on z i. The solution of these differential equations provides the eigenvalues (r i) searched. The results obtained are in accordance with theorem 2 of kinetics (two strictly linear ...
Linearly independent columns of a matrix are important because they allow us to solve for unique solutions to systems of equations. If the columns were linearly dependent, the system would have infinite solutions, making it impossible to solve. ...
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