Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
We have, A = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]` and B = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`
∴ BA = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)] [(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`
= `[(6, 0, 0),(0, 6, 0),(0, 0, 6)]`
= 6I
∴ B–1 = `"A"/6 = 1/6 [(2, 2, -4),(-4, 2, -4),(2, -1, 5)]` ....(i)
Given system of equation is:
x – y = 3
2x + 3y + 4z = 17
And y + 2z = 7
or `[(1, -1, 0),(2, 3, 4),(0, 1, 2)] [(x),(y),(z)] = [(3),(17),(7)]`
∴ `[(x),(y),(z)] = [(1, -1, 0),(2, 3, 4),(0, 1, 2)]^-1 [(3),(17),(7)]`
= `1/6 [(2, 2, -4),(-4, 2, -4),(2, -1, 5)] [(3),(17),(7)]`
= `1/16 [(6 + 34 - 28),(-12 + 34 - 28),(6 - 17 + 35)]`
= `1/6 [(12),(-6),(24)]`
= `[(2),(-1),(4)]`
∴ x = 2, y = –1 and z = 4
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:
`|(1,0,0),(0,1,0),(0,0,1)|`
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 second row, evaluate Δ = `|(5,3,8),(2,0,1),(1,2, 3)|`.
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:
\[A = \begin{bmatrix}1 & - 3 & 2 \\ 4 & - 1 & 2 \\ 3 & 5 & 2\end{bmatrix}\]
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 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.
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.
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))`
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 multiplication completes the calculation of a cofactor?
For \[\begin{vmatrix}1&-2\\4&3\end{vmatrix}\], what is \(M_{11}\)?
For \[\begin{vmatrix}1&-2\\4&3\end{vmatrix}\], what is \(M_{12}\)?
Which expression gives determinant expansion along row \(i\)?
Which expression gives determinant expansion along column \(j\)?
For \(i\ne k\), which mixed row/column property is correct?
