Advertisements
Advertisements
प्रश्न
Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:
\[A = \begin{bmatrix}1 & - 3 & 2 \\ 4 & - 1 & 2 \\ 3 & 5 & 2\end{bmatrix}\]
Advertisements
उत्तर
\[M_{11} = \begin{vmatrix}- 1 & 2 \\ 5 & 2\end{vmatrix} = - 2 - 10 = - 12\]
\[ M_{21 =} \begin{vmatrix}- 3 & 2 \\ 5 & 2\end{vmatrix} = - 6 - 10 = - 16\]
\[ M_{31 =} \begin{vmatrix}- 3 & 2 \\ - 1 & 2\end{vmatrix} = - 6 + 2 = - 4\]
\[ C_{11} = \left( - 1 \right)^{1 + 1} M_{11} = - 12\]
\[ C_{21 =} \left( - 1 \right)^{2 + 1} M_{21} = - \left( - 16 \right) = 16\]
\[ C_{31} = \left( - 1 \right)^{3 + 1} M_{31} = - 4\]
\[D = 1\left( - 12 \right) + 3\left( 8 - 6 \right) + 2\left( 20 + 3 \right) = - 12 + 6 + 46 = 40\]
APPEARS IN
संबंधित प्रश्न
Write Minors and Cofactors of the elements of the following determinant:
`|(2,-4),(0,3)|`
Write Minors and Cofactors of the elements of the following determinant:
`|(1,0,0),(0,1,0),(0,0,1)|`
Using Cofactors of elements of third column, evaluate Δ = `|(1,x,yz),(1,y,zx),(1,z,xy)|`.
If Δ = `|(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 the value of Δ is given by ______.
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:
\[A = \begin{bmatrix}- 1 & 4 \\ 2 & 3\end{bmatrix}\]
Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:
\[A = \begin{bmatrix}1 & a & bc \\ 1 & b & ca \\ 1 & c & ab\end{bmatrix}\]
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
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.
Write \[A^{- 1}\text{ for }A = \begin{bmatrix}2 & 5 \\ 1 & 3\end{bmatrix}\]
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.
Find A–1 if A = `[(0, 1, 1),(1, 0, 1),(1, 1, 0)]` and show that A–1 = `("A"^2 - 3"I")/2`.
Using matrix method, solve the system of equations
3x + 2y – 2z = 3, x + 2y + 3z = 6, 2x – y + z = 2.
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 ______.
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°))`
Find the minor of 6 and cofactor of 4 respectively in the determinant `Delta = abs ((1,2,3),(4,5,6),(7,8,9))`
For a square matrix \(A=[a_{ij}]\) of order \(n\), what is the minor \(M_{ij}\) of \(a_{ij}\)?
After deleting the \(i\)-th row and \(j\)-th column from a square matrix of order \(n\), what is the order of the remaining matrix used to calculate \(M_{ij}\)?
The cofactor \(C_{ij}\) (or \(A_{ij}\)) of \(a_{ij}\) is which quantity?
Which operation is performed immediately after selecting \(a_{ij}\) to find \(M_{ij}\)?
What calculation gives the resulting value \(M_{ij}\) after the required row and column have been deleted?
After finding the minor \(M_{ij}\), what is the next step to find the cofactor \(C_{ij}\)?
For \[\begin{vmatrix}1&-2\\4&3\end{vmatrix}\], what is \(M_{21}\)?
For \[\begin{vmatrix}1&-2\\4&3\end{vmatrix}\], what is \(A_{11}\)?
Which expression gives determinant expansion along row \(i\)?
