The top row of matrix A (1, 2, 1) is multiplied with the first column of matrix B (1,0,-1) and the result is 1x1 + 2x0 + 1x -1 = 0 this is row 1 column 1 of the resultant matrix The top row of matrix A (1,2,1) is multiplied with the second column of matrix B (-1, -1, 1) and the result is 1 x-1 + 2 x -1 + 1 x 1 = -2 , this is row 1 column 2 of the resultant matrix Repeat with the second row of matrix A (-1,-1.-2) x (1,0,-1) = 1 this is row 2 column 1 of the resultant matrix, multiply the second row of A (-1,-1,-2) x (-1,-1,1) = 0, this is row 2 column 2 of the resultant Repeat with the third row of matrix A( -1,1,-2) x (1,0, -1) = 1, this is row 3 column 1 of the resultant the third row of A (-1,1,-2) x( -1,-1,1) = -2, this is row 3 column 2 of the resultant matrix
The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.
Their speed is (8 mi)/(2 h) = 4 mi/h.
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<em>Additional comment</em>
Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...
c² = a² +b² . . . square of hypotenuse is sum of squares of legs
c² = 1² +1² . . . . both legs are 1 in our example triangle
c² = 2
c = √2
That is, the hypotenuse is √2 times the leg length.
