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Which of the following transformations are linear?

Verify which of the following transformations are linear. $T_1(x_1,x_2,x_3) = (x_1,0,x_3)$ $T_2(x_1,x_2)=(2x_1 – 3x_2,x_1 +4,5x_2)$ $T_3(x_1,x_2,x_3)=(1,x_2,x_3)$ $T_4(x_1,x_2)=(4x_1 – 2x_2,3|x_2|)$ $T_5(x_1,x_2,x_3)=(x_1,x_2,-x_3)$ The objective of this question is to find the linear transformation from the given transformation. Read moreFind a nonzero vector orthogonal to the plane through the points P, Q, and R, and area of the […]

Find the dimension of the subspace spanned by the given vectors:

[ begin{bmatrix} 2 \ 4 \ 0 end{bmatrix} , begin{bmatrix} -1\ 6 \ 2 end{bmatrix} , begin{bmatrix} 1 \ 5 \ -3 end{bmatrix} , begin{bmatrix} 7 \ 2 \ 3 end{bmatrix} ] The question aims to find the dimension of the subspace spanned by the given column vectors. Read moreFind a nonzero vector orthogonal to […]

Find the scalar and vector projections of b onto a. a=i+j+k, b=i−j+k

The aim of this question is to find the Scalar and Vector Projection of the given two vectors. The basic concept behind this article is the understanding of Scalar and Vector Projections of vector quantities and how to calculate them. Read moreFind a nonzero vector orthogonal to the plane through the points P, Q, and […]