Consider the matrices. what are the dimensions of the project matrix of two of these matrices
1 answer:
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Answer:
A. Solutions are: x = 2, y = 1.
B. Solutions are: x = 3, y = 2.
C.
1. Inconsistent
2. Inconsistent
3. Consistent
Step-by-step explanation:
A. Solutions of each system of linear equations by substitution method:
Equation 1: 3x - 2y = 4
Equation 2: x = 2y
<u>Step 1:</u> Substitute x = 2y into the Equation 1:
3(2y) - 2y = 4
6y - 2y = 4
4y = 4
Step 2: Divide both sides of the equation by 4 to isolate y:
y = 1.
<u>Step 3:</u> For Equation 2, x = 2y, substitute y = 1 into the equation to solve for x:
x = 2y
x = 2(1)
x = 2
Therefore, the solutions are: x = 2, y = 1.
B. Find the solutions of each system of linear equations by elimination method:
Equation 1: 2x + y = 8
Equation 2: x + y = 5
<u>Step 1:</u> Multiply Equation 2 by 2:
2(x + y) = 5(2)
2x + 2y = 10
<u>Step 2:</u> Subtract Equation 1 from the equation derived from Step 1, 2x + 2y = 10:
2x + 2y = 10
- <u>2x + y = 8</u>
y = 2
Step 3: Plug in y = 2 into Equation 1, 2x + y = 8 to solve for x:
2x + y = 8
2x + (2) = 8
<u>Step 4:</u> subtract both sides of the equation by 2 to isolate x:
2x + 2 - 2 = 8 - 2
2x = 6
<u>Step 5:</u> Divide both sides of the equation by 2 to solve for x:
x = 3.
The solutions are: x = 3, y = 2.
C:
1. Inconsistent
2. Inconsistent
3. Consistent (infinitely many solutions)