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Vector Form Linear Equation Algebra

This post categorized under Vector and posted on August 4th, 2019.

Solve the system of linear equations and give the vector form for the general solution. Midterm exam of linear algebra (Math 2568) at the Ohio State University.The two given equations represent planes and the required line is their intersection. They can be written in vector form as (xyz)cdot U 8 (xyz)cdot V 15 where U (11-1) and V (221) are vectors that are normal to the two planes. It is obvious (I think) that the line is parallel to the cross product vector U times V. So we can use (a_2 b_2 c_2) U times V.We will also quickly look at how to write a system of equations that is equivavectort to a given vector equation and vice versa as well as how to create or force a vector to be a linear combination of a set of given vectors. Lastly we will answer some foundational questions dealing with Vector Equations Linear Combinations and the Spanning Set.

And as we study more and more linear algebra were going to start extending these to multiple dimensions. Obviously we can visualize up to three dimensions. In four dimensions it becomes more abstract. And thats why this type of a notation is useful. Because its very hard to draw a 4 5 or 20 dimensional arrow like this.Solution using inverse beginalign Ax & b A-1Ax & A-1b x & A-1b endalign Wont worry here about how to compute inverse but its very siminp.linargr to the standard method for solving linear equationsThe key is to find a single solution to the non-vectorgeneous which can be done by Gaussian elimination if such a solution exists. The general solution is then this solution plus any linear combination of solutions to the vectorgeneous equation.

Writing linear equations using the vector-intercept form Writing linear equations using the point-vector form and the standard form Parallel and perpendicular lines

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