Advertisements
Advertisements
प्रश्न
Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:
\[A = \begin{bmatrix}0 & 2 & 6 \\ 1 & 5 & 0 \\ 3 & 7 & 1\end{bmatrix}\]
Advertisements
उत्तर
\[M_{11} = \begin{vmatrix}5 & 0 \\ 7 & 1\end{vmatrix} = 5 - 0 = 5\]
\[ M_{21} = \begin{vmatrix}2 & 6 \\ 7 & 1\end{vmatrix} = 2 - 42 = - 40\]
\[ M_{31} = \begin{vmatrix}2 & 6 \\ 5 & 0\end{vmatrix} = 0 - 30 = - 30\]
\[ C_{11} = \left( - 1 \right)^{1 + 1} M_{11} = 5\]
\[ C_{21} = \left( - 1 \right)^{2 + 1} M_{21} = - \left( - 40 \right)\]
\[ C_{31} = \left( - 1 \right)^{3 + 1} M_{31} = - 30\]
\[D = 0\left( 5 - 0 \right) - 2\left( 1 - 0 \right) + 6\left( 7 - 15 \right) = - 2 - 48 = - 50\]
APPEARS IN
संबंधित प्रश्न
Write Minors and Cofactors of the elements of the following determinant:
`|(a,c),(b,d)|`
Write Minors and Cofactors of the elements of the following determinant:
`|(1,0,4),(3,5,-1),(0,1,2)|`
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 ______.
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`
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:
\[A = \begin{bmatrix}a & h & g \\ h & b & f \\ g & f & c\end{bmatrix}\]
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 \[A^{- 1}\text{ for }A = \begin{bmatrix}2 & 5 \\ 1 & 3\end{bmatrix}\]
Find A–1 if A = `[(0, 1, 1),(1, 0, 1),(1, 1, 0)]` and show that A–1 = `("A"^2 - 3"I")/2`.
If A = `[(1, 2, 0),(-2, -1, -2),(0, -1, 1)]`, find A–1. Using A–1, solve the system of linear equations x – 2y = 10, 2x – y – z = 8, –2y + z = 7.
Using matrix method, solve the system of equations
3x + 2y – 2z = 3, x + 2y + 3z = 6, 2x – y + z = 2.
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 =` ____________.
Find the minor of 6 and cofactor of 4 respectively in the determinant `Delta = abs ((1,2,3),(4,5,6),(7,8,9))`
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?
What is the first step to find the minor \(M_{ij}\)?
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 \(M_{11}\)?
How does the determinant value change when expansion is performed along a different row or column?
For \(i\ne k\), which mixed row/column property is correct?
