QUESTION 1 The coordinate vector of the vector (1.2.2) in the basis B=(u= (1,1,1); v= (1,0,1); w=(0,0,1))is: OA (2,1,3) OB (2,-1,1) OC (1.2.-1) OD. (1,2,2)
What is Basis of a Vector Space:
The set B of vectors in the vector space V is referred to as a basis in mathematics if every member of V can be written in a unique way as a finite linear combination of components of B. The coefficients of this linear combination are the elements, or coordinates, of the vector with respect to B. Basis components are referred to as basis vectors. A set B is a basis if all of its members are linearly independent and every element of V is a linear combination of all of its members. A basis is a spanning set that is linearly independent, to put it another way. In a vector space, several bases are possible, but they all have the same number.
Given:
Given vector is and given basis is .
To Determine:
We determine the coordinate of the vector relative to the basis.
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