2. Create the following matrix A:

(a) Create a matrix B by extracting the first column of matrix A.

(b) Create a matrix C by extracting the second row of matrix A.

(c) Use colon operator to create a matrix D by extracting the first through third columns of matrix A.

(d) Create a singled valued matrix E by extracting the value from second row, third column of matrix A i.e. A_2,3.

(e) Create a matrix F by extracting the values of elements A_1,3 , A_2,4 , and A_3,5 and combining them into a single matrix.

3. Compute the total mass of the following components, using a dot product:

Component	Density	Volume
Propellant	1.2 g/cm3	700 cm3
Steel	7.8 g/cm3	200 cm3
Aluminum	2.7 g/cm3	300 cm3

4. Solve the following systems of equations using both the matrix left division and inverse matrix methods:

(a) -2x + y= -3; x + y = 3;

(b) 10x - 7y = 7; -3x + 2y +6z = 4; 5x + y +5z = 6;

(c) x + 4y-z+w = 2; 2x +7y+z -2w = 16; x +4y -z -2w = -15; 3x -10y -2z +5w = -14;

5. Given the array A = [-1, 3; 4, 2], raise A to second power by array exponentiation (same as element-by-element). Raise A to second power by matrix exponentiation. Explain why the answers are different.

3.4 > 2.1 > 0.5 > 6.5 > 4.2 4.2 > 7.7 > 3.4 > 4.5 > 3.9 8.9 > 8.3 > 1.5 > 3.4 > 3.9