Advertisements
Advertisements
Question
Write Minors and Cofactors of the elements of following determinants:
`|(1,0,0),(0,1,0),(0,0,1)|`
Solution
Minors:
`M_11 = abs ((1,0),(0,1)) = 1 - 0 = 1`
`M_12 = abs ((0,0),(0,1)) = 0`
`M_13 = abs ((0,1),(0,0)) = 0,`
`M_21 = abs ((0,0),(0,1)) = 0`
`M_22 = abs((1,0),(0,1)) = 1`
`M_23 = abs ((1,0),(0,0)) = 0`
`M_31 = abs ((0,0),(1,0)) = 0`
`M_32 = abs ((1,0),(0,0)) = 0`
`M_33 = abs ((1,0),(0,1)) = 1`
Cofactors:
`A_11 = (-1)^(1 + 1) M_11 = 1`
`A_12 = (-1)^(1 + 2) M_12 = (- 1) xx 0 = 0`
`A_13 = (-1)^(1 + 3) M_13 = 1 xx 0 = 0`
`A_21 = (-1)^(2 + 1) M_21 = 0`
`A_22 = (-1)^(2 + 2) M_22 = 1`
`A_23 = (-1)^(2 + 3) M_23 = 0`
`A_31 = (-1)^(3 + 1) M_31 = 0`
`A_32 = (-1)^(3 + 2) M_32 = 0`
`A_33 = (-1)^(3 + 3) M_33 = 1 * 1 = 1`
APPEARS IN
RELATED QUESTIONS
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)|`
Write Minors and Cofactors of the elements of following determinants:
`|(1,0,4),(3,5,-1),(0,1,2)|`
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 `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 ______.
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:
\[A = \begin{bmatrix}- 1 & 4 \\ 2 & 3\end{bmatrix}\]
Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:
\[A = \begin{bmatrix}1 & - 3 & 2 \\ 4 & - 1 & 2 \\ 3 & 5 & 2\end{bmatrix}\]
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.
Write \[A^{- 1}\text{ for }A = \begin{bmatrix}2 & 5 \\ 1 & 3\end{bmatrix}\]
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.
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.
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 =` ____________.
`abs(("cos" 15°, "sin" 15°),("sin" 75°, "cos" 75°))`
