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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?
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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.
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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?
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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.
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