Question

1. Find -5A + 4B
A=[6, 1, -4, -6, 7, -7] B=[-5, -1, -3, -8, 6, 8]

a. [-10, 9, 8, -2, 16, 67]
b. -10, 9, 8, -2, -59, -68]
c. [-50, -9, -1, 16, -11, -68]
d. [-50, -9, 8, -2, -11, 67]

2. Solve the matrix equation.
2X + 2 [2, -8, -4, 2] =[4, -6, 2, -8]
a. [0, 5, -3, -2]
b. [0, -11, -3, -6]
c. [0, 5, 5, -6]
d. [4, 5, 5, -2]

3. Find the product.
[-5,-2,
-8, -5]

[-5, 7,
-9, -5]

a. [ 25, 18, -35, 10]
b. [43, -25, 85, -31]
c. [40, 45, -56, 25]
d. [43, -25, -31, 85]

4. determine whether the product is defined or undefined. if defined, give the dimensions of the product matrix.
[1, 1, -4, [9, 1, -7]
5, 6, 0]

a. defined; 3 x 3
b. defined; 2 x 1
c. defined; 2 x 3
d. undefined

Answer 1

1.) A = [6, 1, -4, -6, 7, -7] B = [-5, -1, -3, -8, 6, 8]
-5A + 4B = -5[6, 1, -4, -6, 7, -7] + 4[-5, -1, -3, -8, 6, 8] = [-30, -5, 20, 30, -35, 35] + [-20, -4, -12, -32, 24, 32] = [-50, -9, 8, -2, -11, 67]

2.) 2X + 2[2, -8, -4, 2] = [4, -6, 2, -8]
2X + [4, -16, -8, 4] = [4, -6, 2, -8]
2X = [4, -6, 2, -8] - [4, -16, -8, 4] = [0, 10, 10, -12]
X = [0/2, 10/2, 10/2, -12/2] = [0, 5, 5, -6]
X = [0, 5, 5, -6]


3.)
[-5,-2, * [-5, 7,  = [25 + 18,  -35 + 10,  =  [43, -25,
-8, -5]    -9, -5]     40 + 45,  -56 + 25]        85, -31]

4.)
[1, 1, 4,  *  [9, 
 5, 6, 0]      1,
                  -7]
=> 2 x 3 * 3 x 1
since the inner dimensions is equal = 3, the product is defined and the dimension of the product is the outer dimensions 2 x 1