Answer:
x = 2 and y = 10.
Step-by-step explanation:
To solve the given system of equations using the matrix conversion method, we can represent the equations in matrix form as follows:
[A] [X] = [B],
where
[A] is the coefficient matrix of the variables x and y,
[X] is the column matrix of variables x and y,
and [B] is the column matrix of constants.
For the given system of equations:
a) 3x - 4y = 4,
b) x + 2y = 8,
The coefficient matrix [A] is:
[3 -4]
[1 2]
The column matrix [X] is:
[x]
[y]
The column matrix [B] is:
[4]
[8]
Now, we can solve for [X] using matrix operations.
First, we need to find the inverse of matrix [A]. If it exists, we can multiply both sides of the equation by [A]⁻¹.
[A]⁻¹ [A] [X] = [A]⁻¹ [B],
Simplifying, we get:
[X] = [A]⁻¹ [B].
To find [A]⁻¹, we invert the coefficient matrix [A].
[A]⁻¹ = (1/det[A]) [adj[A]],
where det[A] is the determinant of [A] and adj[A] is the adjugate of [A].
Calculating the determinant of [A]:
det[A] = (3 * 2) - (-4 * 1) = 6 + 4 = 10.
Next, we find the adjugate of [A]:
adj[A] = [2 4]
[1 3].
Now, we can calculate [A]⁻¹:
[A]⁻¹ = (1/10) [2 4]
Multiplying [A]⁻¹ with [B]:
[X] = [A]⁻¹ [B] = (1/10) [2 4] [4] = (1/10) [20] = [2],
[1 3] [8] [10]
Therefore, the solution to the system of equations is:
x = 2,
y = 10.
Thus, the solution to the given system of equations is x = 2 and y = 10.
Solve this equation by matrix conversion method.
a) 3x-4y=4
b) x+2y=8
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Answers & Comments
Answer:
x = 2 and y = 10.
Step-by-step explanation:
To solve the given system of equations using the matrix conversion method, we can represent the equations in matrix form as follows:
[A] [X] = [B],
where
[A] is the coefficient matrix of the variables x and y,
[X] is the column matrix of variables x and y,
and [B] is the column matrix of constants.
For the given system of equations:
a) 3x - 4y = 4,
b) x + 2y = 8,
The coefficient matrix [A] is:
[3 -4]
[1 2]
The column matrix [X] is:
[x]
[y]
The column matrix [B] is:
[4]
[8]
Now, we can solve for [X] using matrix operations.
First, we need to find the inverse of matrix [A]. If it exists, we can multiply both sides of the equation by [A]⁻¹.
[A]⁻¹ [A] [X] = [A]⁻¹ [B],
Simplifying, we get:
[X] = [A]⁻¹ [B].
To find [A]⁻¹, we invert the coefficient matrix [A].
[A]⁻¹ = (1/det[A]) [adj[A]],
where det[A] is the determinant of [A] and adj[A] is the adjugate of [A].
Calculating the determinant of [A]:
det[A] = (3 * 2) - (-4 * 1) = 6 + 4 = 10.
Next, we find the adjugate of [A]:
adj[A] = [2 4]
[1 3].
Now, we can calculate [A]⁻¹:
[A]⁻¹ = (1/10) [2 4]
[1 3].
Multiplying [A]⁻¹ with [B]:
[X] = [A]⁻¹ [B] = (1/10) [2 4] [4] = (1/10) [20] = [2],
[1 3] [8] [10]
Therefore, the solution to the system of equations is:
x = 2,
y = 10.
Thus, the solution to the given system of equations is x = 2 and y = 10.
Verified answer
Answer:
Solve this equation by matrix conversion method.
a) 3x-4y=4
b) x+2y=8
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