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Find the rank of the matrix for the following equations :
3x + 4y – z – 6w = 0
2x + 3y + 2z – 3w = 0
2x + y – 14z – 9w = 0
x + 3y + 13z + 3w = 0
3x + 4y – z – 6w = 0
2x + 3y + 2z – 3w = 0
2x + y – 14z – 9w = 0
x + 3y + 13z + 3w = 0
Correct answer is '2'. Can you explain this answer?
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Verified Answer
Find the rank of the matrix for the following equations :3x + 4y &ndas...
Let A be the coefficient matrix, i.e., consider,
∴ The rank of the matrix is 2.
∴ The rank of the matrix is 2.
The correct answer is: 2
Most Upvoted Answer
Find the rank of the matrix for the following equations :3x + 4y &ndas...
To determine the rank of the matrix for the given equations, we need to write the equations in matrix form. Assuming the equations are 3x + 4y = 0, the matrix form of the equations is:
[3 4] * [x y] = [0]
The matrix on the left represents the coefficients of the variables x and y, while the matrix on the right represents the constant term. To find the rank of the matrix, we perform row reduction on the augmented matrix:
[3 4 | 0]
Using row operations, we can subtract 3 times the first row from the second row:
[3 4 | 0]
[0 -12 | 0]
Now, we can divide the second row by -12 to simplify the matrix:
[3 4 | 0]
[0 1 | 0]
The matrix is now in row echelon form. We can see that there are two non-zero rows, which means the rank of the matrix is 2.
[3 4] * [x y] = [0]
The matrix on the left represents the coefficients of the variables x and y, while the matrix on the right represents the constant term. To find the rank of the matrix, we perform row reduction on the augmented matrix:
[3 4 | 0]
Using row operations, we can subtract 3 times the first row from the second row:
[3 4 | 0]
[0 -12 | 0]
Now, we can divide the second row by -12 to simplify the matrix:
[3 4 | 0]
[0 1 | 0]
The matrix is now in row echelon form. We can see that there are two non-zero rows, which means the rank of the matrix is 2.
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Find the rank of the matrix for the following equations :3x + 4y – z – 6w = 02x + 3y + 2z – 3w = 02x + y – 14z – 9w = 0x + 3y + 13z + 3w = 0Correct answer is '2'. Can you explain this answer?
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Find the rank of the matrix for the following equations :3x + 4y – z – 6w = 02x + 3y + 2z – 3w = 02x + y – 14z – 9w = 0x + 3y + 13z + 3w = 0Correct answer is '2'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Find the rank of the matrix for the following equations :3x + 4y – z – 6w = 02x + 3y + 2z – 3w = 02x + y – 14z – 9w = 0x + 3y + 13z + 3w = 0Correct answer is '2'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the rank of the matrix for the following equations :3x + 4y – z – 6w = 02x + 3y + 2z – 3w = 02x + y – 14z – 9w = 0x + 3y + 13z + 3w = 0Correct answer is '2'. Can you explain this answer?.
Find the rank of the matrix for the following equations :3x + 4y – z – 6w = 02x + 3y + 2z – 3w = 02x + y – 14z – 9w = 0x + 3y + 13z + 3w = 0Correct answer is '2'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Find the rank of the matrix for the following equations :3x + 4y – z – 6w = 02x + 3y + 2z – 3w = 02x + y – 14z – 9w = 0x + 3y + 13z + 3w = 0Correct answer is '2'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the rank of the matrix for the following equations :3x + 4y – z – 6w = 02x + 3y + 2z – 3w = 02x + y – 14z – 9w = 0x + 3y + 13z + 3w = 0Correct answer is '2'. Can you explain this answer?.
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