Question

Compute utimes​u, vtimes​u, and StartFraction v times u Over u times u EndFraction using the vectors uequals[Start 2 By 1 Matrix 1st Row 1st Column negative 1 2nd Row 1st Column 4 EndMatrix ]and vequals[Start 2 By 1 Matrix 1st Row 1st Column 7 2nd Row 1st Column 5 EndMatrix ]

Answer 1

u•u = 17

u•v = 13

v•u = u•v = 17

v•u/u•u = 13/17

Explanation:

Given 2 column matrices

u = [-1 4] and v = [7 5]

Note that when computing product, we will multiply component wise.

To compute u times u, we will take the dot product of both column matrix.

u•u = [-1 4] • [-1 4]

u•u = (-1)(-1) + (4)(4)

u•u = 1+16

u•u = 17

To compute u times v, we will take the dot product of column matrix u and column matrix v.

u•v = [-1 4] • [7 5]

u•v = (-1)(7) + (4)(5)

u•v = -7+20

u•v = 13

v•u/u•u can be gotten by simply substituting the resulting values.

v•u/u•u = 13/17