Find the matrix B of T with respect to the basis B = {~u1, ~u2}, where u1 is a unit vector that points along y = x toward increasing x and y and ~u2 is a unit vector that is perpendicular to ~u1 and 90 degrees counterclockwise from ~u1.

The matrix B is given as

Step-by-step explanation:

As the vectors are given by u1 and u2 where u1 is given as

As y=x thus

So the value of x and y is given as

Thus u_1 is given as

Now the vector u_2 is given as perpendicular to u_1 i.e.

So the B matrix is given as

So the matrix B is as above.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47