Transformation is defined as T(x)=Ax, find whether x is unique or not. [A=begin{bmatrix} 1 & -5 & -7\ 3 & 7 & 5end{bmatrix}] [B=begin{bmatrix} 2\ 2end{bmatrix}] This question aims to find the uniqueness of vector $x$ with the help of linear transformation. This question uses the concept of Linear transformation with reduced row echelon form. Reduced row echelon form […]

# Category Archives: Vectors Q&A

[ boldsymbol{ B = left{ Bigg [ begin{array}{c} 1 \ -2 \ 5 end{array} Bigg ] , Bigg [ begin{array}{c} 3 \ 0 \ -1 end{array} Bigg ] , Bigg [ begin{array}{c} 8 \ -2 \ 7 end{array} Bigg ] right} } ] The aim of this question is to find the change-of-coordinates matrix given […]

The aim of this question is to become familiar with the vector representation. Two vectors are given in this question and their product needs to be found. After that, the visual representation of the origin is also made. This question is based on the concepts of physics. Vectors are quantities that have magnitude as well […]

[ y = begin {bmatrix} 5 \ 3 end {bmatrix} ] [ u = begin {bmatrix} 4 \ 9 end {bmatrix} ] The question aims to find the distance between vector y to the line through u and the origin. The question is based on the concept of vector multiplication, dot product, and orthogonal projection. […]

[ R(t) = < t^{2}, frac{2}{3} t^{3} , t > text {and point} < 4, frac{-16}{3}, -2 > ] This question aims to determine the tangent vector, normal vector, and the binormal vector of any given vector. The tangent vector T is a vector that is tangent to the given surface or vector at any […]