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Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .
statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1
statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,
- a)Statement 1 is False, Statement 2 is true
- b)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statement
- c)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .
- d)Statement 1 is true, Statement 2 is false.
Correct answer is option 'D'. Can you explain this answer?
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Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity...
⇒ So by (2) c,d cannot be zero.
so if
Most Upvoted Answer
Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity...
The statement (1) is not correct. The correct statement should be:
If A^2 = I, then tr(A) = 0 or tr(A) = 2.
Explanation:
If A^2 = I, then (A^2 - I) = 0.
This can be factored as (A - I)(A + I) = 0.
Since matrix multiplication is not commutative, we cannot conclude that A - I = 0 or A + I = 0.
However, we can conclude that the determinant of (A - I)(A + I) is 0, which means the determinant of A - I or A + I is 0.
If the determinant of A - I is 0, then tr(A) - 2 = 0, so tr(A) = 2.
If the determinant of A + I is 0, then tr(A) + 2 = 0, so tr(A) = -2.
Therefore, tr(A) can be either 2 or -2, not necessarily 0 as stated in statement (1).
If A^2 = I, then tr(A) = 0 or tr(A) = 2.
Explanation:
If A^2 = I, then (A^2 - I) = 0.
This can be factored as (A - I)(A + I) = 0.
Since matrix multiplication is not commutative, we cannot conclude that A - I = 0 or A + I = 0.
However, we can conclude that the determinant of (A - I)(A + I) is 0, which means the determinant of A - I or A + I is 0.
If the determinant of A - I is 0, then tr(A) - 2 = 0, so tr(A) = 2.
If the determinant of A + I is 0, then tr(A) + 2 = 0, so tr(A) = -2.
Therefore, tr(A) can be either 2 or -2, not necessarily 0 as stated in statement (1).
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Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct answer is option 'D'. Can you explain this answer?
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Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct 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 be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct 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 be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct answer is option 'D'. Can you explain this answer?.
Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct 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 be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct 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 be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct answer is option 'D'. Can you explain this answer?.
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Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let A be A 2 * 2 matrix with real entries. Let i be the 2 x 2 Identity matrix. Denote by tr (A), the sum of diagonal entries o f A. Assume A2 = I .statement (1 ) : If A ≠ i and A ≠ - i , then det A = -1statement (2 ) : If A ≠ I and A ≠ - I , then tr (A) ≠ 0 Then,a)Statement 1 is False, Statement 2 is trueb)Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for statementc)Statement 1 is a true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 .d)Statement 1 is true, Statement 2 is false.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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