Advertisements
Advertisements
प्रश्न
Write Minors and Cofactors of the elements of the following determinant:
`|(1,0,4),(3,5,-1),(0,1,2)|`
Advertisements
उत्तर
`|(1,0,4),(3,5,-1),(0,1,2)|`
Minors:
M11 = `|(5,-1),(1,2)|`
= 5 × 2 − (−1) × 1
= 10 + 1
= 11
M12 = `|(3,-1),(0,2)|`
= 3 × 2 − (−1) × 0
= 6 + 0
= 6
M13 = `|(3,5),(0,1)|`
= 3 × 1 − 5 × 0
= 3 − 0
= 3
M21 = `|(0,4),(1,2)|`
= 0 × 2 − 1 × 4
= 0 − 4
= −4
M22 = `|(1,4),(0,2)|`
= 1 × 2 − 4 × 0
= 2 − 0
= 2
M23 = `|(1,0),(0,1)|`
= 1 × 1 − 0 × 0
= 1 − 0
= 1
M31 = `|(0,4), (5, -1)|`
= (−1) × 0 − 4 × 5
= 0 − 20
= −20
M32 = `|(1,4),(3,-1)|`
= 1 × (−1) − 3 × 4
= (−1) − 12
= −13
M33 = `|(1,0),(3,5)|`
= 1 × 5 − 0 × 3
= 5 − 0
= 5
Cofactors:
A11 = (−1)1+1 M11
= 11 × 1
= 11
A12 = (−1)1+2 M12
= (−1) × 6
= −6
A13 = (−1)1+3 M13
= 1 × 3
= 3
A21 = (−1)2+1 M21
= (−1) × (−4)
= 4
A22 = (−1)2+2 M22
= 1 × 2
= 2
A23 = (−1)2+3 M23
= (−1) × 1
= −1
A31 = (−1)3+1 M31
= 1 × (−20)
= −20
A32 = (−1)3+2 M32
= (−1) × (−13)
= −13
A33 = (−1)3+3 M33
= 1 × 5
= 5
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:
`|(a,c),(b,d)|`
Write Minors and Cofactors of the elements of the following determinant:
`|(1,0,0),(0,1,0),(0,0,1)|`
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:
\[A = \begin{bmatrix}1 & - 3 & 2 \\ 4 & - 1 & 2 \\ 3 & 5 & 2\end{bmatrix}\]
Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:
\[A = \begin{bmatrix}1 & a & bc \\ 1 & b & ca \\ 1 & c & ab\end{bmatrix}\]
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
Write the adjoint of the matrix \[A = \begin{bmatrix}- 3 & 4 \\ 7 & - 2\end{bmatrix} .\]
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 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°))`
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 \(M_{ij}\)?
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 \(M_{11}\)?
For \[\begin{vmatrix}1&-2\\4&3\end{vmatrix}\], what is \(M_{12}\)?
For \[\begin{vmatrix}1&-2\\4&3\end{vmatrix}\], what is \(M_{21}\)?
For \[\begin{vmatrix}1&-2\\4&3\end{vmatrix}\], what is \(M_{22}\)?
For \[\begin{vmatrix}1&-2\\4&3\end{vmatrix}\], what is \(A_{11}\)?
Which expression gives determinant expansion along row \(i\)?
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?
