All vectors and subspaces are in r^n.

check the true statements below:

a. for each y and each subspace w, the vector y - proj_w (y) is orthogonal to w.

b. if z is orthogonal to u_1 and u_2 and if w = span{u_1, u_2}. then z must be in w.

c. the orthogonal projection y of y onto a subspace w can sometimes depend on the orthogonal basis for w used to compute y.

d. if y is in a subspace w, then the orthogonal projection of y onto w is y itself.

e. if the columns of an n times p matrix u are orthonormal, then uu^t y is the orthogonal projection of y onto the column space of u

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1

the answer is 99.