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.

answer: do we write it

step-by-step explanation:

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!