Solve for x and y begin{bmatrix}x & 2y 4 & 6 end{bmatrix}=begin{bmatrix}2 & -2 2x & -6y end{bmatrix} 3begin{bmatrix}x & y y & x end{bmatrix}=begin{bma

generals336 2020-11-08 Answered
Solve for x and y [x2y46]=[222x6y]
3[xyyx]=[6996]
2[xyx+yxy]=[2426]
[xyyx][yxxy]=[4466]
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Expert Answer

Demi-Leigh Barrera
Answered 2020-11-09 Author has 97 answers
Step 1
Answer(43):
Given that,
[x2y46]=[222x6y]
Two matrices are said to be equal if each corresponding entry is equal. Therefore, equating the corresponding entries of the left and right sides matrice x=2
And
2y=2
y=22
y=1
Hence, the solution of the given equation is x=2, y=-1
Step 2
Answer(44):
Given that, 3[xyyx]=[6996]
Since k[abcd]=[akbkckdk]
So , [3x3y3y3x]=[6996]
Two matrices are said to be equal if each corresponding entry is equal.
Therefore, equating the corresponding entries of the left and right sides matrices.
3x=6
x=63
x=2
3y=9
y=93
y=3
Hence, the solution of the given equation is x=2, y=-3
Step 3
Answer(45):
Given that, 2[xyx+yxy]=[2426]
Since k[abcd]=[akbkckdk]
So , [2x2y2(x+y)2(xy)]=[2426]
Two matrices are said to be equal if each corresponding entry is equal.
Therefore, equating the corresponding entries of the left and right sides matrices
2x=2
x=22
x=1
2y=4
y=42
y=2
Hence, the solution of the given equation is x=1, y=-2
Step 4
Answer(46):
Given that, [xyyx][yxxy]=[4466]
To find the solution, Apply the matrices property [abcd][pqrs]=[apbqcrds]
[xyyxyxx=y]=[4466]
Two matrices are said to be equal if each corresponding entry is equal.
Therefore, equating the corresponding entries of the left and right sides matrices.
(1) x-y=4
(2) x+y=6
Now, add the equation (1) and (2).
2x=10
x=5
And, subtract the equation (1) and (2).
2y=46
2y=2
y=1
Hence, the solution of the given equation is x=5, y=1
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Jeffrey Jordon
Answered 2022-01-23 Author has 2047 answers

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