GATE Exam > GATE Questions > 10. Let A = [aij] be an nxnmztrix with real e...
Start Learning for Free
10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true?
Most Upvoted Answer
10. Let A = [aij] be an nxnmztrix with real entries such that the sum ...
Analysis of Statements regarding Matrix A
Statement 1: A is non-singular
If the sum of all entries in each row of matrix A is zero, it implies that the rows of A are linearly dependent. Therefore, the determinant of A is zero, making A singular. Hence, Statement 1 is false.
Statement 2: A is singular
As explained above, the rows of matrix A are linearly dependent due to the sum of entries being zero in each row. This makes the determinant of A zero, leading to A being singular. Therefore, Statement 2 is true.
Statement 3: 0 is an eigenvalue of A
Since A is singular, the determinant of A is zero. This implies that 0 is an eigenvalue of A. Therefore, Statement 3 is true.
Therefore, the correct answer is:
(c) 2 & 3 are true.
Statement 1: A is non-singular
If the sum of all entries in each row of matrix A is zero, it implies that the rows of A are linearly dependent. Therefore, the determinant of A is zero, making A singular. Hence, Statement 1 is false.
Statement 2: A is singular
As explained above, the rows of matrix A are linearly dependent due to the sum of entries being zero in each row. This makes the determinant of A zero, leading to A being singular. Therefore, Statement 2 is true.
Statement 3: 0 is an eigenvalue of A
Since A is singular, the determinant of A is zero. This implies that 0 is an eigenvalue of A. Therefore, Statement 3 is true.
Therefore, the correct answer is:
(c) 2 & 3 are true.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true?
Question Description
10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true?.
10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true?.
Solutions for 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? defined & explained in the simplest way possible. Besides giving the explanation of
10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true?, a detailed solution for 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? has been provided alongside types of 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? theory, EduRev gives you an
ample number of questions to practice 10. Let A = [aij] be an nxnmztrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements : (1) A is non-singular (2) A is singular (3) 0 is an eigen value of A Which of the following is correct ? (a) Only 1 is true (b) 1 & 3 are true (c) 2 & 3 are true? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup