Explain the reasining Explain the difference between a scalar and a vector. How

Question

Explain the reasining

Explain the difference between a scalar and a vector. How do vectors and matrices differ? Explain why a system of equations cannot have exactly two unique solutions. Explain how back-substitution is used in conjunction with row reduction to solve a system of linear equations. Compare how the solution to a vector equations, matrix equation, and augmented matrix are related. What is the geometric description of one vector? What about two linearly independent vectors? What about two linearly dependent vectors? What is the relationship between basic variables and free variables and whether a consistent system has a dependent or independent solution? How do we describe a line or plane through the origin using the term "span" using vectors? In the programming language of your choice, write a function called row_op which operates on a matrix to row reduce the second row using the first row. Assume the pivot is in the first position in the first row. Use remark statements to explain how the program works. You may want to use your calculator's programming language.

Explanation / Answer

1. vectors have magnitude and direction , scalars have only magnitude. matrices are made up of multiple vectors as their row or coloumn 2. for more than 1 unique solution , all the straight lines representing the equations will have to intersect at more than one point which is impossible . hence the case 3. First in row reduction , rows are eliminated in such a way that only a single varible is at bottom , 2 in the row above and so on. hence first we get the value of the lowest variable . then we put it in the eqn obtained from row above to get the other variable and so on . this is back substitution. 4.

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