Class 8 Exam > Class 8 Questions > Read the given statements carefully and state... Start Learning for Free
Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.
(ii) The inverse of a non-singular matrix always exists.
(iii) If a matrix is singular, its determinant is zero.
(i) (ii) (iii)
(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.
(ii) The inverse of a non-singular matrix always exists.
(iii) If a matrix is singular, its determinant is zero.
(i) (ii) (iii)
- a)(i)-T, (ii)-F, (iii)-T
- b)(i)-F,(ii)- T, (iii)-F
- c)(i)-T, (ii)-T, (iii)-T
- d)(i)-F, (ii)-F, (iii)-T
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Read the given statements carefully and state T for true and F for fal...
(i) The determinant of a 2x2 matrix [a b; c d] is indeed ad - bc, which is correct.
(ii) The inverse of a non-singular matrix (a matrix with a non-zero determinant) always exists, which is also correct.
(iii) If a matrix is singular, its determinant is zero, which is correct.
(ii) The inverse of a non-singular matrix (a matrix with a non-zero determinant) always exists, which is also correct.
(iii) If a matrix is singular, its determinant is zero, which is correct.
Most Upvoted Answer
Read the given statements carefully and state T for true and F for fal...
Understanding the Statements
Let's analyze each statement regarding matrices to determine their truth values.
Statement (i): The determinant of a 2x2 matrix [a b; c d] is ad - bc.
- This statement is True.
- The formula for the determinant of a 2x2 matrix is indeed calculated as ad - bc.
Statement (ii): The inverse of a non-singular matrix always exists.
- This statement is True.
- A non-singular matrix is one that has a non-zero determinant, which guarantees that an inverse can be calculated.
Statement (iii): If a matrix is singular, its determinant is zero.
- This statement is True.
- A singular matrix is defined as one that does not have an inverse, which occurs when its determinant equals zero.
Conclusion
Thus, evaluating each statement gives us:
- (i) - T
- (ii) - T
- (iii) - T
Therefore, the correct option is (c): (i) - T, (ii) - T, (iii) - T.
This reflects a solid understanding of matrix properties, crucial for solving mathematical problems related to linear algebra.
Let's analyze each statement regarding matrices to determine their truth values.
Statement (i): The determinant of a 2x2 matrix [a b; c d] is ad - bc.
- This statement is True.
- The formula for the determinant of a 2x2 matrix is indeed calculated as ad - bc.
Statement (ii): The inverse of a non-singular matrix always exists.
- This statement is True.
- A non-singular matrix is one that has a non-zero determinant, which guarantees that an inverse can be calculated.
Statement (iii): If a matrix is singular, its determinant is zero.
- This statement is True.
- A singular matrix is defined as one that does not have an inverse, which occurs when its determinant equals zero.
Conclusion
Thus, evaluating each statement gives us:
- (i) - T
- (ii) - T
- (iii) - T
Therefore, the correct option is (c): (i) - T, (ii) - T, (iii) - T.
This reflects a solid understanding of matrix properties, crucial for solving mathematical problems related to linear algebra.
 | Explore Courses for Class 8 exam |  |
Top Courses for Class 8View all
Top Courses for Class 8
Question Description
Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer?.
Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 8. Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free.
Here you can find the meaning of Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Read the given statements carefully and state T for true and F for false.(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.(ii) The inverse of a non-singular matrix always exists.(iii) If a matrix is singular, its determinant is zero.(i) (ii) (iii)a)(i)-T, (ii)-F, (iii)-Tb)(i)-F,(ii)- T, (iii)-Fc)(i)-T, (ii)-T, (iii)-Td)(i)-F, (ii)-F, (iii)-TCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 8 tests.
| Explore Courses for Class 8 exam | |
Top Courses for Class 8
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
