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Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1?
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Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 ...
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Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 ...
Solution:
Finding AB:
To find AB, we need to perform matrix multiplication of A and B. The result will be a 3x3 matrix.
AB = AxB
= (-4x1 + 4x1 + 4x2) (-4x(-1) + 4x(-2) + 4x3) (-4x1 + 4x1 + 4x1)
( -7x1 + 1x1 + 3x2) (-7x(-1) + 1x(-2) + 3x3) (-7x1 + 1x1 + 3x1)
( 5x1 - 3x1 - 1x2) ( 5x(-1) - 3x(-2) - 1x3) ( 5x1 - 3x1 - 1x1)
= (2 - 4 2) (-4 11 -3) (2 - 4 2)
(-3 13 -4) (-8 11 2) (-3 13 -3)
(2 -6 2) (-13 11 -7) (2 -6 1)
= matrix 2 -4 2 -3 13 -4 2 -6 2 -13 11 -7 2 -6 1
Solving the system of linear equations:
To solve the system of linear equations using AB, we need to set up the augmented matrix [AB|C], where C is the matrix of constants.
For the first system of linear equations:
[AB|C] = matrix
2 -4 2 4
-3 13 -4 9
2 -6 2 1
By performing row operations, we can reduce this matrix to row echelon form:
matrix
1 0 0 -1
0 1 0 1
0 0 1 -2
Therefore, the solution to the first system of linear equations is x=-1, y=1, and z=-2.
For the second system of linear equations:
[AB|C] = matrix
2 -4 2 4
-3 13 -4 9
2 -6 1 -1
By performing row operations, we can reduce this matrix to row echelon form:
matrix
1 0 0 -1
0 1 0 1
0 0 1 -2/3
Therefore, the solution to the second system of linear equations is x=-1, y=1, and z=-2/3.
Finding AB:
To find AB, we need to perform matrix multiplication of A and B. The result will be a 3x3 matrix.
AB = AxB
= (-4x1 + 4x1 + 4x2) (-4x(-1) + 4x(-2) + 4x3) (-4x1 + 4x1 + 4x1)
( -7x1 + 1x1 + 3x2) (-7x(-1) + 1x(-2) + 3x3) (-7x1 + 1x1 + 3x1)
( 5x1 - 3x1 - 1x2) ( 5x(-1) - 3x(-2) - 1x3) ( 5x1 - 3x1 - 1x1)
= (2 - 4 2) (-4 11 -3) (2 - 4 2)
(-3 13 -4) (-8 11 2) (-3 13 -3)
(2 -6 2) (-13 11 -7) (2 -6 1)
= matrix 2 -4 2 -3 13 -4 2 -6 2 -13 11 -7 2 -6 1
Solving the system of linear equations:
To solve the system of linear equations using AB, we need to set up the augmented matrix [AB|C], where C is the matrix of constants.
For the first system of linear equations:
[AB|C] = matrix
2 -4 2 4
-3 13 -4 9
2 -6 2 1
By performing row operations, we can reduce this matrix to row echelon form:
matrix
1 0 0 -1
0 1 0 1
0 0 1 -2
Therefore, the solution to the first system of linear equations is x=-1, y=1, and z=-2.
For the second system of linear equations:
[AB|C] = matrix
2 -4 2 4
-3 13 -4 9
2 -6 1 -1
By performing row operations, we can reduce this matrix to row echelon form:
matrix
1 0 0 -1
0 1 0 1
0 0 1 -2/3
Therefore, the solution to the second system of linear equations is x=-1, y=1, and z=-2/3.
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Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1?
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Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1?.
Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1?.
Solutions for Given that,, A= matrix -4 4 4 -7 1 3 5 -3 -1 and B=matrix 1 -1 1 1 -2 -2 2 1 3 Find AB. Use this result to solve the following system of linear equations 1) x-y z=4 x-2y-2z=9 2x y 3z=1 2) -4x-7y 5z=4 4x y-3z=9 4x 3y-z=1? in English & in Hindi are available as part of our courses for Class 12.
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