scalar product

Kinematics..

Find the scalar product of - 4 and the square matrix ( 5 0 - 4 5 ) . => ( 20 0 16 20 ) or ( - 20 0 16 - 20 ) or ( - 20 0 16 20 ) or ( 20 0 16 - 20 )..

Find the scalar product of - 5 and the square matrix ( 4 0 - 6 3 ) . => ( - 5 0 5 5 ) or ( - 4 3 - 4 0 ) or ( - 20 0 30 - 15 ) or ( - 4 - 3 - 6 0 )..

. orders of factors in a vector product is important. This is not true for scalars because, the order of factors in algebra or arithmetic does n..

. The first case, that is, multiplication of a vector by a scalar has been dealt with in the section; multiplication of vectors by real numbers. Hence, we move on to the second case, that is, multiplication of two vectors in such a way as to yield a scalar. Such an operation is ..

. If the right hand is held so that the curled fingers follow the rotation of , the extended right thumb will point in the direction of . orders of factors in a vector product is important. This is not true for scalars because, the order of factors in algebra or arithmetic does ..

The following are the Operation on Real Functions: Sum Function, Difference Function, Product Function, Quotient Function, Scalar Multiplication Function, Composite Functions, Inverse Function..

Types of linear systems Gauss-Jordan elimination, Gauss-Jordan method Vectors and vector addition Geometrical solution sets of systems of equations Rectangular matrices to row echelon form Matrix multiplication Inverse to a square matrix Determinants of 2 by 2 and 3 by 3 matrices Row redu..

(A T ) T = A (A + B) T = A T + B T , A and B being of the same order. (KA) T = KA T , k be any scalar (real or complex) (AB) T = B T A T ; A and B being conformable for the product A..

Ampere's law is a useful relation that is analogous to Gauss's law. Ampere's law is a relationship between the tangential component of magnetic field at points on a closed curve and the net current through the area bounded by the curve. Ampere's law is formulated in terms of the line integral of ..