(3+5+2+4+4+4 22 points) Let A= [1 1 1] [1 1 1]
[0 1 1]
[0 1 1]

Required:
a. Find a basis for the column space of A. What is the dimension of this basis?
b. Use Gram-Schmidt to find an orthonormal basis for the column space of A: {q1, q2, q3}
c. Find a fourth vector q4 that completes the basis you have found in part (a) to an orthonormal basis of R4. To which of the 4 fundamental spaces related to A does q4 belong to?
d. Find the projection matrix P that maps any vector onto C(A). What is the projection of b= (1, 0, 0,0) onto this space?

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5

thus, the first answer choice, y = sec x, is the correct one