Mathematics Exam > Mathematics Questions > let A = [ aij]be a 3x3 invertible matrix with...
Start Learning for Free
let A = [ aij] be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:
If there exist a matrix X with Constant elements such that A X = B, then X is
If there exist a matrix X with Constant elements such that A X = B, then X is
- a)Skew symmetric
- b)Null Matrix
- c)Diagonal matrix
- d)Symmetric matrix
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bi...
Now ginen A is invertiable ⇒ |A| ≠ 0 and A-1 exit and AX = B
and
Most Upvoted Answer
let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bi...
Explanation:
To find the matrix X, we need to solve the equation AX = B, where A is a 3x3 invertible matrix and B is a matrix formed by taking the sum of all elements in each row of A, except the corresponding diagonal element.
Let's consider the given matrix A:
A = [aij]
We can write the equation AX = B as:
[ a11 a12 a13 ] [ x11 x12 x13 ] [ b11 b12 b13 ]
[ a21 a22 a23 ] * [ x21 x22 x23 ] = [ b21 b22 b23 ]
[ a31 a32 a33 ] [ x31 x32 x33 ] [ b31 b32 b33 ]
Expanding the product, we get:
a11*x11 + a12*x21 + a13*x31 = b11
a11*x12 + a12*x22 + a13*x32 = b12
a11*x13 + a12*x23 + a13*x33 = b13
a21*x11 + a22*x21 + a23*x31 = b21
a21*x12 + a22*x22 + a23*x32 = b22
a21*x13 + a22*x23 + a23*x33 = b23
a31*x11 + a32*x21 + a33*x31 = b31
a31*x12 + a32*x22 + a33*x32 = b32
a31*x13 + a32*x23 + a33*x33 = b33
We can rearrange these equations in matrix form as:
[ a11 a12 a13 ] [ x11 x12 x13 ] [ b11 b12 b13 ]
[ a21 a22 a23 ] * [ x21 x22 x23 ] = [ b21 b22 b23 ]
[ a31 a32 a33 ] [ x31 x32 x33 ] [ b31 b32 b33 ]
This equation can be solved using the inverse of matrix A:
X = A^(-1) * B
Since A is an invertible matrix, its inverse exists. Therefore, we can find the matrix X by multiplying the inverse of A with B.
Answer:
The matrix X obtained by solving the equation AX = B is a symmetric matrix.
To find the matrix X, we need to solve the equation AX = B, where A is a 3x3 invertible matrix and B is a matrix formed by taking the sum of all elements in each row of A, except the corresponding diagonal element.
Let's consider the given matrix A:
A = [aij]
We can write the equation AX = B as:
[ a11 a12 a13 ] [ x11 x12 x13 ] [ b11 b12 b13 ]
[ a21 a22 a23 ] * [ x21 x22 x23 ] = [ b21 b22 b23 ]
[ a31 a32 a33 ] [ x31 x32 x33 ] [ b31 b32 b33 ]
Expanding the product, we get:
a11*x11 + a12*x21 + a13*x31 = b11
a11*x12 + a12*x22 + a13*x32 = b12
a11*x13 + a12*x23 + a13*x33 = b13
a21*x11 + a22*x21 + a23*x31 = b21
a21*x12 + a22*x22 + a23*x32 = b22
a21*x13 + a22*x23 + a23*x33 = b23
a31*x11 + a32*x21 + a33*x31 = b31
a31*x12 + a32*x22 + a33*x32 = b32
a31*x13 + a32*x23 + a33*x33 = b33
We can rearrange these equations in matrix form as:
[ a11 a12 a13 ] [ x11 x12 x13 ] [ b11 b12 b13 ]
[ a21 a22 a23 ] * [ x21 x22 x23 ] = [ b21 b22 b23 ]
[ a31 a32 a33 ] [ x31 x32 x33 ] [ b31 b32 b33 ]
This equation can be solved using the inverse of matrix A:
X = A^(-1) * B
Since A is an invertible matrix, its inverse exists. Therefore, we can find the matrix X by multiplying the inverse of A with B.
Answer:
The matrix X obtained by solving the equation AX = B is a symmetric matrix.
|
Explore Courses for Mathematics exam
|
|
let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer?
Question Description
let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer?.
let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer?.
Solutions for let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice let A = [ aij]be a 3x3 invertible matrix with real entries and B = [bij] be a matrix which is formed such that bij is the sum of all the elements except aij in the ith row. Answer the following:If there exist a matrix X with Constant elements such that A X = B, then X isa)Skew symmetricb)Null Matrixc)Diagonal matrixd)Symmetric matrixCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup