Let A be an n times m matrix, let vector b elementof E^n and let vector u, vector w, (both in E^m) be solutions to the matrix equation A vector x = vector b. 1 If vector v = vector u - vector w use the properties of matrix multiplication to show that: A(t vector v) = vector 0_E^n for any real number t. vector u + t vector v is a solution to the matrix equation A vector x = vector b for any real number t. Solution 1. A(tv)=tAv=tA(u-w)=tAu-tAw=tb-tb=0 We used the linearity of matrix multiplication here. 2. A(u+tv)=Au+A(tv)=b+0=b HEre we used: A(tv)=0 for any real number t from part 1. Hence proved.

1. Part A Spacecraft instruments measure the radiation from an asteroid, and the data show that the
power per unit wavelength peaks at 40 m Assuming the asteroid is a blackbody, find its surface
temperature Express your answer using two significant figures. ST- Submit Incorrect; Try
Again; 4 attempts remaining
Solution
Here,
34.18)
wavelength = 40 um
let the temperature is T
Using Wien's displcement law
wavlength = b/T
40 *10^-6 = (2.898 *10^-3)/T
solving for T
T = 72.45 K
the temperature of the surafce is 72.45 K