Home
Class 12
MATHS
Which of the following is not correct in...

Which of the following is not correct in a given determinant of `A ,` where `A=([a_(i j)])_(3x3)`

A. Order of minor is less than order of the det(A)
B. Minor of an element can never be equal to cofactor of the same element
C. Value of a determinant is obtained by multiplying elements of a row or column by corresponding cofactors
D. Order of minors and cofactors of elements of A is same

Text Solution

AI Generated Solution

To solve the question, we need to analyze each of the given options regarding determinants and identify which one is not correct. Let's go through each option step-by-step. ### Step 1: Understanding the Options 1. **Option A:** Order of minor is less than order of the determinant. - A minor is obtained by deleting one row and one column from the determinant. For a 3x3 determinant, the order of the minor will be 2 (since it becomes a 2x2 matrix). Therefore, this statement is correct. 2. **Option B:** Minor of an element can never be equal to cofactor of the same element. ...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos
  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

Find minors and cofactors of all the elements of the determinant |[1,-2],[ 4 ,3]|

If A is square matrix of order 3, then which of the following is not true ? a.| A ' | = | A | b. | k A | = k 3 | A | c. minor of an element of |A| can never be equal cofactor of the same element d. order of minors and of cofactors of elements of |A| is same

The sum of the products of the elements of any row of a matrix A with the corresponding cofactors of the elements of the same row is always equal to

Write the minor and cofactor of each element of the following determinants and also evaluate the determinant in each case: |[5,-10],[0,3]|

Elementary Transformation of a matrix: The following operation on a matrix are called elementary operations (transformations) 1. The interchange of any two rows (or columns) 2. The multiplication of the elements of any row (or column) by any nonzero number 3. The addition to the elements of any row (or column) the corresponding elements of any other row (or column) multiplied by any number Echelon Form of matrix : A matrix A is said to be in echelon form if (i) every row of A which has all its elements 0, occurs below row, which has a non-zero elements (ii) the first non-zero element in each non –zero row is 1. (iii) The number of zeros before the first non zero elements in a row is less than the number of such zeros in the next now. [ A row of a matrix is said to be a zero row if all its elements are zero] Note: Rank of a matrix does not change by application of any elementary operations For example [(1,1,3),(0,1,2),(0,0,0)],[(1,1,3,6),(0,1,2,2),(0,0,0,0)] are echelon forms The number of non-zero rows in the echelon form of a matrix is defined as its RANK. For example we can reduce the matrix A=[(1,2,3),(2,4,7),(3,6,10)] into echelon form using following elementary row transformation. (i) R_2 to R_2 -2R_1 and R_3 to R_3 -3R_1 [(1,2,3),(0,0,1),(0,0,1)] (ii) R_2 to R_2 -2R_1 [(1,2,3),(0,0,1),(0,0,0)] This is the echelon form of matrix A Number of nonzero rows in the echelon form =2 rArr Rank of the matrix A is 2 The echelon form of the matrix [(1,3,4,3),(3,9,12,9),(1,3,4,1)] is :

Elementary Transformation of a matrix: The following operation on a matrix are called elementary operations (transformations) 1. The interchange of any two rows (or columns) 2. The multiplication of the elements of any row (or column) by any nonzero number 3. The addition to the elements of any row (or column) the corresponding elements of any other row (or column) multiplied by any number Echelon Form of matrix : A matrix A is said to be in echelon form if (i) every row of A which has all its elements 0, occurs below row, which has a non-zero elements (ii) the first non-zero element in each non –zero row is 1. (iii) The number of zeros before the first non zero elements in a row is less than the number of such zeros in the next now. [ A row of a matrix is said to be a zero row if all its elements are zero] Note: Rank of a matrix does not change by application of any elementary operations For example [(1,1,3),(0,1,2),(0,0,0)],[(1,1,3,6),(0,1,2,2),(0,0,0,0)] are echelon forms The number of non-zero rows in the echelon form of a matrix is defined as its RANK. For example we can reduce the matrix A=[(1,2,3),(2,4,7),(3,6,10)] into echelon form using following elementary row transformation. (i) R_2 to R_2 -2R_1 and R_3 to R_3 -3R_1 [(1,2,3),(0,0,1),(0,0,1)] (ii) R_2 to R_2 -2R_1 [(1,2,3),(0,0,1),(0,0,0)] This is the echelon form of matrix A Number of nonzero rows in the echelon form =2 rArr Rank of the matrix A is 2 Rank of the matrix [(1,1,1),(1,-1,-1),(3,1,1)] is :

Elementary Transformation of a matrix: The following operation on a matrix are called elementary operations (transformations) 1. The interchange of any two rows (or columns) 2. The multiplication of the elements of any row (or column) by any nonzero number 3. The addition to the elements of any row (or column) the corresponding elements of any other row (or column) multiplied by any number Echelon Form of matrix : A matrix A is said to be in echelon form if (i) every row of A which has all its elements 0, occurs below row, which has a non-zero elements (ii) the first non-zero element in each non –zero row is 1. (iii) The number of zeros before the first non zero elements in a row is less than the number of such zeros in the next now. [ A row of a matrix is said to be a zero row if all its elements are zero] Note: Rank of a matrix does not change by application of any elementary operations For example [(1,1,3),(0,1,2),(0,0,0)],[(1,1,3,6),(0,1,2,2),(0,0,0,0)] are echelon forms The number of non-zero rows in the echelon form of a matrix is defined as its RANK. For example we can reduce the matrix A=[(1,2,3),(2,4,7),(3,6,10)] into echelon form using following elementary row transformation. (i) R_2 to R_2 -2R_1 and R_3 to R_3 -3R_1 [(1,2,3),(0,0,1),(0,0,1)] (ii) R_2 to R_2 -2R_1 [(1,2,3),(0,0,1),(0,0,0)] This is the echelon form of matrix A Number of nonzero rows in the echelon form =2 rArr Rank of the matrix A is 2 Rank of the matrix [(1,1,1,-1),(1,2,4,4),(3,4,5,2)] is :

Which of the following species have same bond order and same shape (a) N_(3)^(Θ) (b) O_(3) (c ) CO_(2) (d) NO_(2)^(Θ) .

Write Minors and Cofactors of the elements of following determinants: (i) |(2,-4),( 0 ,3)| (ii) |(a ,c),( b, d)|

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Find the real values of lambda for which the following system of linea...

    Text Solution

    |

  2. If a , b , c are non-zero real numbers and if the system of equations...

    Text Solution

    |

  3. Which of the following is not correct in a given determinant of A , wh...

    Text Solution

    |

  4. Let |x2xx^2x6xx6|=a x^4+b x^3+c x^2+dx+edot Then, the value of 5a+4b+3...

    Text Solution

    |

  5. Let delta=|A x x^2 1 B y y^2 1 C z z^2 1|a n d1=|A B C x y z y z z xx ...

    Text Solution

    |

  6. If Delta1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta2=|[q,-b, y],[-p,...

    Text Solution

    |

  7. Without expanding show that: =|(cose c^2theta,cot^2theta,1),(cot^2thet...

    Text Solution

    |

  8. Find the value of the determinant =|(2, 3, 4),( 5, 6, 8),( 6x,9x ,12 x...

    Text Solution

    |

  9. Without expanding evaluate the determinant |[41,1,5],[79,7,9],[29,5,3]...

    Text Solution

    |

  10. Show that |1a bc1b c+a1c a+b|=0

    Text Solution

    |

  11. Without expanding evaluate the determinant |[(a^x+a^(-x))^2,(a^x-a^(-x...

    Text Solution

    |

  12. If D1=|[1, 1, 1],[x^2,y^2,z^2],[x, y, z]| and D2=|[1, 1, 1],[yz, zx,xy...

    Text Solution

    |

  13. Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2...

    Text Solution

    |

  14. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

    Text Solution

    |

  15. If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0...

    Text Solution

    |

  16. If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

    Text Solution

    |

  17. If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2bal...

    Text Solution

    |

  18. If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...

    Text Solution

    |

  19. Using the factor theorem it is found that a+b , b+c and c+a are thr...

    Text Solution

    |

  20. Let |x^2+3xx-1x+3x+1-2xx-4x-3x+4 3x|=a x^4+b x^3+c x^2+e be an identi...

    Text Solution

    |