हिंदी

Which of the Following is Not Correct in a Given Determinant of A, Where a = [Aij]3×3. - Mathematics

Advertisements
Advertisements

प्रश्न

Which of the following is not correct in a given determinant of A, where A = [aij]3×3.

विकल्प

  • Order of minor is less than order of the det (A)

  • Minor of an element can never be equal to cofactor of the same element

  • Value of determinant is obtained by multiplying elements of a row or column by  corresponding cofactors

  • Order of minors and cofactors of elements of A is same

MCQ

उत्तर

Minor of an element can never be equal to the cofactor of the same element.
\[C_{i j} = \left( - 1 \right)^{i + j} M_{i j} \]
\[\text{ So, for even values of }i + j, C_{i j} = M_{i j} . \]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Determinants - Exercise 6.7 [पृष्ठ ९३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 6 Determinants
Exercise 6.7 | Q 4 | पृष्ठ ९३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find values of x, if ` |(2,4),(5,1)|=|(2x, 4), (6,x)|`


Using the property of determinants and without expanding, prove that:

`|(x, a, x+a),(y,b,y+b),(z,c, z+ c)| = 0`


Let A be a square matrix of order 3 × 3, then | kA| is equal to

(A) k|A|

(B) k2 | A |

(C) k3 | A |

(D) 3k | A |


Without expanding at any stage, find the value of:

`|(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|`


A matrix A of order 3 × 3 has determinant 5. What is the value of |3A|?

 

On expanding by first row, the value of the determinant of 3 × 3 square matrix
  \[A = \left[ a_{ij} \right]\text{ is }a_{11} C_{11} + a_{12} C_{12} + a_{13} C_{13}\] , where [Cij] is the cofactor of aij in A. Write the expression for its value on expanding by second column.

 

Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. If |A| = 5, write the value of a31 C31  +  a32 C32 a33 C33.


A matrix of order 3 × 3 has determinant 2. What is the value of |A (3I)|, where I is the identity matrix of order 3 × 3.


Which of the following is not correct?


Solve the following system of linear equations using matrix method: 
3x + y + z = 1
2x + 2z = 0
5x + y + 2z = 2


Without expanding, show that Δ = `|("cosec"^2theta, cot^2theta, 1),(cot^2theta, "cosec"^2theta, -1),(42, 40, 2)|` = 0


If Δ = `|(0, "b" - "a", "c" - "a"),("a" - "b", 0, "c" - "b"),("a" - "c", "b" - "c", 0)|`, then show that ∆ is equal to zero.


The determinant ∆ = `|(sqrt(23) + sqrt(3), sqrt(5), sqrt(5)),(sqrt(15) + sqrt(46), 5, sqrt(10)),(3 + sqrt(115), sqrt(15), 5)|` is equal to ______.


The value of the determinant ∆ = `|(sin^2 23^circ, sin^2 67^circ, cos180^circ),(-sin^2 67^circ, -sin^2 23^circ, cos^2 180^circ),(cos180^circ, sin^2 23^circ, sin^2 67^circ)|` = ______.


If a1, a2, a3, ..., ar are in G.P., then prove that the determinant `|("a"_("r" + 1), "a"_("r" + 5), "a"_("r" + 9)),("a"_("r" + 7), "a"_("r" + 11), "a"_("r" + 15)),("a"_("r" + 11), "a"_("r" + 17), "a"_("r" + 21))|` is independent of r.


If a + b + c ≠ 0 and `|("a", "b","c"),("b", "c", "a"),("c", "a", "b")|` 0, then prove that a = b = c.


Prove tha `|("bc" - "a"^2, "ca" - "b"^2, "ab" - "c"^2),("ca" - "b"^2, "ab" - "c"^2, "bc" - "a"^2),("ab" - "c"^2, "bc" - "a"^2, "ca" - "b"^2)|` is divisible by a + b + c and find the quotient.


Let f(t) = `|(cos"t","t", 1),(2sin"t", "t", 2"t"),(sin"t", "t", "t")|`, then `lim_("t" - 0) ("f"("t"))/"t"^2` is equal to ______.


If A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`, then A–1 exists if ______.


There are two values of a which makes determinant, ∆ = `|(1, -2, 5),(2, "a", -1),(0, 4, 2"a")|` = 86, then sum of these number is ______.


If A is invertible matrix of order 3 × 3, then |A–1| ______.


If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.


If A, B, and C be the three square matrices such that A = B + C, then Det A is equal to


`abs ((1 + "a", "b", "c"),("a", 1 + "b", "c"),("a", "b", 1 + "c")) =` ____________


The value of the determinant `abs ((1,0,0),(2, "cos x", "sin x"),(3, "sin x", "cos x"))` is ____________.


Find the minor of the element of the second row and third column in the following determinant `[(2,-3,5),(6,0,4),(1,5,-7)]`


If `"abc" ne 0  "and" abs ((1 + "a", 1, 1),(1, 1 + "b", 1),(1,1,1 + "c")) = 0, "then"  1/"a" + 1/"b" + 1/"c" =` ____________.


Let A be a square matrix of order 2 x 2, then `abs("KA")` is equal to ____________.


Find the 5th term of expansion of `(x^2 + 1/x)^10`?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×