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 all questions*
1. Find -5A + 4B
A=[6, 1, -4, -6, 7, -7] B=[-5, -1, -3, -8, 6, 8]
-5A = [-30, -5, 20, 30, -35, 35]
4B = [-20, -4, -12, -32, 24, 32]
-5A + 4B = [-30, -5, 20, 30, -35, 35] + [-20, -4, -12, -32, 24, 32]
= [-50, -9, 8, -2, -11, 67]
Therefore, the answer is d. [-50, -9, 8, -2, -11, 67]
2. Solve the matrix equation.
2X + 2 [2, -8, -4, 2] =[4, -6, 2, -8]
First, simplify the right side of the equation:
2 [2, -8, -4, 2] = [4, -16, -8, 4]
Now, we have:
2X + [4, -16, -8, 4] = [4, -6, 2, -8]
Subtracting [4, -16, -8, 4] from both sides:
2X = [0, 10, 10, -12]
Dividing by 2:
X = [0, 5, 5, -6]
Therefore, the answer is c. [0, 5, 5, -6]
3. Find the product.
[-5, -2]
[-8, -5]
[-5, 7]
[-9, -5]
Multiplying the matrices:
[(-5)(-5) + (-2)(-9), (-5)(7) + (-2)(-5)]
[(-8)(-5) + (-5)(-9), (-8)(7) + (-5)(-5)]
[43, -25]
[85, -31]
Therefore, the answer is b. [43, -25, 85, -31]
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]
The dimensions of the first matrix are 2 x 3 (2 rows, 3 columns) and the dimensions of the second matrix are 3 x 1 (3 rows, 1 column). To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, the number of columns in the first matrix is 3 while the number of rows in the second matrix is 3, so the product is defined. The dimensions of the product matrix will be 2 x 1 (2 rows, 1 column).
Therefore, the answer is b. defined; 2 x 1