7. OR. If you prefer, calculateProj_CS(A)b using the approach ofExample 8 on page 266 instead. You should get an infinite number ofsolutions for x to the normalequation. Any solution for x will work,and then calculate Ax to get Proj_CS(A)
   • For either approach, briefly explain whyProj_CS(A)b is theclosest vector in your plane to the vector(See Theorem 5.15 if needed.)
8. Choose 5 arbitrary unique vectors inR² that are not on the same line or scalar multiples ofeach other. What are your 5 vectors in R²?
   • Use normal equations (see page 265, if needed)to determine the equation of the least square regression line forthis set of 5 points.
9. Choose any 2 of the 5 vectors in the above problem that willform a nonstandard basis for R², whichwe will call B’. (12 points for entire problem)
   • What are your two vectors in B’?
   • If B is the standard basis for R² (I.e. B ={(1.0).(0.1)}, determine the transition matrix (called P^-1 inour text) from B to B’.
   • Use P^-1 to calculate the coordinates for (1,5) withrespect to the basis B’.
10. Investigate the following linear differentialequation: y’’ + 4y = 0; Solutions {sin(2x),cos(2x)}

• Verify that each solution satisfies the differentialequation.
• Use the Wronskian to verify that the solution set islinearly independent.
• Write the general solution of the differential equation.