Question

We will continue to work on the concepts of basis and dimensions in this homework Again, if necessary, you can use your calculator to compute the rref of a matrix 1 (5 points) Recalled that in Calculus, if the dot product of two vectors is zero, then we know that the two vectors are orthogonal (perpendicular) to each other. That is, if yi 3 y3 then the angle between the two vectors is coS 2 The two vectors z and y are called orthogonal vectors. (Note that the book use || . I to denote the magnitude of a vector) In high school physics, you know that the vector u as shown in the figure below can be projected onto the î and j direction, as liell cos θ and Ilu!! sin θ respectively However, we know that i cannot be projected onto j, and j cannot be projected onto i, They are in a sense "independent" of one another (i) Show that if vectors g and y in R2 are orthogonal and non-zero vectors, then they are linearly independent (ii) We say the three non-zero vectors u, and w in R3 are orthogonal, iffu-u = 0, u w 0, and y-w- 0. Show that if u, y, and w are orthogonal and non-zero, then they are linearly independent My

Answer 1

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