हिंदी

If △=|a11a12a13a21a22a23a31a32a33| and Aij is Cofactors of aij, then value of Δ is given by ______. - Mathematics

Advertisements
Advertisements

प्रश्न

If `triangle = |(a_11,a_12,a_13),(a_21,a_22,a_23),(a_31,a_32,a_33)|` and Aij is Cofactors of aij, then value of Δ is given by ______.

विकल्प

  • a11 A31+ a12 A32 + a13 A33

  • a11 A11+ a12 A21 + a13 A31

  • a21 A11+ a22 A12 + a23 A13

  • a11 A11+ a21 A21 + a31 A31

MCQ
रिक्त स्थान भरें

उत्तर

If `triangle = |(a_11,a_12,a_13),(a_21,a_22,a_23),(a_31,a_32,a_33)|` and Aij is Cofactors of aij, then value of Δ is given by a11 A11+ a21 A21 + a31 A31.

Explanation:

∆ = the sum of the product of the elements of a row or column and their corresponding super-parts

C1 Components of a column (a11, a21, a31)

Cofactors A11, A21, A31

⇒ ∆ = a11 A11 + a21 A21 + a31 A31

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Determinants - Exercise 4.4 [पृष्ठ १२६]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 4 Determinants
Exercise 4.4 | Q 5 | पृष्ठ १२६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Write Minors and Cofactors of the elements of following determinants:

`|(2,-4),(0,3)|`


Write Minors and Cofactors of the elements of following determinants:

`|(a,c),(b,d)|`


Using Cofactors of elements of second row, evaluate `triangle = |(5,3,8),(2,0,1),(1,2, 3)|`


Using Cofactors of elements of third column, evaluate `triangle = |(1,x,yz),(1,y,zx),(1,z,xy)|`


if A =  `((2,3,10),(4,-6,5),(6,9,-20))`, Find `A^(-1)`. Using `A^(-1)` Solve the system of equation `2/x + 3/y +10/z = 2`; `4/x - 6/y + 5/z = 5`; `6/x + 9/y - 20/z = -4`


Using matrices, solve the following system of equations :

2x - 3y + 5z = 11

3x + 2y - 4z = -5

x + y - 2z = -3


Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:

\[A = \begin{bmatrix}5 & 20 \\ 0 & - 1\end{bmatrix}\]


Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:

\[A = \begin{bmatrix}1 & - 3 & 2 \\ 4 & - 1 & 2 \\ 3 & 5 & 2\end{bmatrix}\]


Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:

\[A = \begin{bmatrix}0 & 2 & 6 \\ 1 & 5 & 0 \\ 3 & 7 & 1\end{bmatrix}\]


Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:

\[A = \begin{bmatrix}a & h & g \\ h & b & f \\ g & f & c\end{bmatrix}\]


Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:

\[A = \begin{bmatrix}2 & - 1 & 0 & 1 \\ - 3 & 0 & 1 & - 2 \\ 1 & 1 & - 1 & 1 \\ 2 & - 1 & 5 & 0\end{bmatrix}\]


If \[A = \begin{vmatrix}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{vmatrix}\]  and Cij is cofactor of aij in A, then value of |A| is given 




Write the adjoint of the matrix \[A = \begin{bmatrix}- 3 & 4 \\ 7 & - 2\end{bmatrix} .\]


If Cij is the cofactor of the element aij of the matrix \[A = \begin{bmatrix}2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7\end{bmatrix}\], then write the value of a32C32.


If \[A = \begin{bmatrix}5 & 6 & - 3 \\ - 4 & 3 & 2 \\ - 4 & - 7 & 3\end{bmatrix}\] , then write the cofactor of the element a21 of its 2nd row.


If `"A" = [(1,1,1),(1,0,2),(3,1,1)]`, find A-1. Hence, solve the system of equations x + y + z = 6, x + 2z = 7, 3x + y + z = 12.


Given A = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`, B = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`, find BA and use this to solve the system of equations y + 2z = 7, x – y = 3, 2x + 3y + 4z = 17.


If A is a matrix of order 3 × 3, then number of minors in determinant of A are ______.


The sum of the products of elements of any row with the co-factors of corresponding elements is equal to ______.


If A `= [(0,1,1),(1,0,1),(1,1,0)] "then"  ("A"^2 - 3"I")/2 =` ____________.


Evaluate the determinant `Delta = abs (("log"_3  512, "log"_4  3),("log"_3  8, "log"_4  9))`


`abs(("cos"  15°, "sin"  15°),("sin"  75°, "cos"  75°))`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×