Four non –zero vectors will always be a.  linearly dependent                 b. linearly independent c. either a or b                           d. none of these

IF barx and bary non zero linearly independent vectors such that |barx + bary|=|barx -bary| then

Examine whether the following vectors from a linearly dependent or independent set of vector: hati+3hatj+5hatk, 2hati+6hatj+10hatk

VECTOR ALGEBRA | LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE | Definition and physical interpretation: Linear Combination, Linear Combination: Linear Independence And Linear Dependence, Linearly Independent, Linearly Dependent, Theorem 1: If veca and vecb are two non collinear vectors; then every vector vecr coplanar with veca and vecb can be expressed in one and only one way as a linear combination: x veca +y vecb ., Theorem 2: If veca , vecb and vecc are non coplanar vectors; then any vector vecr can be expressed as linear combination: x veca +y vecb +z vecc , Theorem 3:If vectors veca , vecb and vecc are coplanar then det( veca vecb vecc ) = 0, Examples: Prove that the segment joining the middle points of two non parallel sides of a trapezium is parallel to the parallel sides and half of their sum., Components of a vector in terms of coordinates of its end points

Show that the vectors hati-3hatj+2hatk,2hati-4hatj-hatk and 3hati+2hatj-hatk and linearly independent.

Rank of a non zero matrix is always (A) 0 (B) 1 (C) gt1 (D) gt0

Given four non zero vectors bar a,bar b,bar c and bar d . The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :

In which of the following type of matrix inverse does not exist always? a. idempotent b. orthogonal c. involuntary d. none of these

In which of the following type of matrix inverse does not exist always? a. idempotent b. orthogonal c. involuntary d. none of these

Examine whether the following vectors from a linearly dependent or independent set of vector: veca=(1,-2,30),vecb=(-2,3,-4),vecc=(1,-1,5)

If a,b and c are three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a( lamda being some non-zero scalar), then a+2b+6c is equal to