(i) Use the projection formula V(V¹V)-¹VT to verify that the orthogonal projection matrix onto the z- 0 0 axis in 3 dimensional space R³ is given by. 0 0 0 1 (ii) Using the first four digits of your code number: a,b,c,d; why is the system of equations: ax + by = 1 cx + dy = 2 (a + c)x+ (b + d)y = 4 obviously inconsistent? Find the least squares solution to this system of equations. (iii) Explain how the theory of orthogonal projections relates to your solution in (ii).

Q: 2(3y-5)=34

A: We will see the ans in next step

Q: +b); A= 135, B = 10, b = 5

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Q: -12 = 4m + 4

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Q: y + 8 = 12 y =

A: when left side digit shift to right side then it becomes negative if digit is positive and vice…

Q: y + 9=18

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Q: 4x + 7 = 27

A: We have the equation,                           4x + 7 = 27 We want to solve the equation by finding…

Q: 18x+26=22

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Q: answer 3y+8=14

A: The given equation is: 3y+8=14  To find the value of y.

Q: 3b-4=28-b b=?

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Q: -2g + = 3g - 37

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Q: n=o entl

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Q: 4x+7+2x+5=180

A: Given equation ,   4x + 7 + 2x + 5 = 180

Q: 5x+9=24

A: Since nothing is mentioned about the operation  to be performed on the above given equation, I will…

Q: -16m+8m=340

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Q: z2-3z=-8

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Q: -3(4x-5)-6=18

A: Given: −34x−5−6=18 To determine: The value of x.

Q: d2-5d-20=0

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Q: 4=2v-14

A: The given equation is,

Q: Vx +7 = -3

A: We have to solve for x.

Q: 3x-2=13

A: Given equation is 3x-2=13

Q: 3x-2=7

A: Any linear equation in one variable can be solved by taking all the terms other than those…