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Consider the following statements I. D...

Consider the following statements
I. Determinant is a square matrix.
II. Determinant is a number associated with a square matrix.
Which of the above statement(s) is/are correct ?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

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AI Generated Solution

The correct Answer is:
To solve the question, we need to evaluate the two statements regarding determinants and determine which ones are correct. ### Step-by-Step Solution: 1. **Understanding the First Statement:** - The first statement is: "Determinant is a square matrix." - This statement is **incorrect**. A determinant itself is not a square matrix; rather, it is a value that can be calculated from a square matrix. A determinant is defined only for square matrices (matrices with the same number of rows and columns), but it is not a matrix itself. 2. **Understanding the Second Statement:** - The second statement is: "Determinant is a number associated with a square matrix." - This statement is **correct**. The determinant is indeed a numerical value that is computed from a square matrix. It provides important information about the matrix, such as whether it is invertible. 3. **Conclusion:** - From the analysis above, we can conclude that: - Statement I is incorrect. - Statement II is correct. - Therefore, the correct answer is that only statement II is true. ### Final Answer: - The correct statement is: **Only Statement II is correct.**
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PUNEET DOGRA-DETERMINANTS -PREV YEAR QUESTIONS
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  3. Consider the following statements I. Determinant is a square matrix....

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  4. If |(a,b,0),(0,a,b),(b,0,a)| = 0, then which one of the following is c...

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  5. If a ne b ne c all are positive, then the value of determinant |(a,b,c...

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  6. If any two adjacent rows or columns of a determinant are interchanged ...

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  7. The determinant of a skew symmetric matrix of odd order is

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  8. If C(ij) is the cofactor of the element a(ij) of the determinant |{:(2...

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  9. What is the value of the determinant |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,a...

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  10. If D is determinant of order 3 and D' is the determinant obtained by r...

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  11. Consider the following statements I. A matrix is not a number. II....

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  12. The roots of the equation |(1,t-1,1),(t-1,1,1),(1,1,t-1)| = 0 are

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  13. The value of the determinant |(m,n,p),(p,m,n),(n,p,m)|

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  14. If each element in a row of a determinant is multiplied by the same fa...

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  15. If two rows (or column) are identical or Proportional the value of the...

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  16. If |(8,-5,1),(5,x,1),(6,3,1)| = 2, then what is the value of x ?

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  17. If A = ((1,2),(2,3))and = ((1,0),(1,0)), then what is the value of det...

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  18. What is the value of |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))| ?

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  19. What is the value of |(1,omega,2 omega^(2)),(2,2omega^(2),4 omega^(3))...

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  20. The root of the equation |(x,alpha,1),(beta,x,1),(beta,gamma,1)| = 0 a...

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