हिंदी

In the Following Matrix Equation Use Elementary Operation R2 → R2 + R1 and the Equation Thus Obtained: [ 2 3 1 4 ] [ 1 0 2 − 1 ] = [ 8 − 3 9 − 4 ] - Mathematics

Advertisements
Advertisements

प्रश्न

In the following matrix equation use elementary operation R2 → R2 + Rand the equation thus obtained:

\[\begin{bmatrix}2 & 3 \\ 1 & 4\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 9 & - 4\end{bmatrix}\]
Advertisements

उत्तर

\[\begin{bmatrix}2 & 3 \\ 1 & 4\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 9 & - 4\end{bmatrix}\]

By applying elementary operation R2 → R2 + R1, we get

\[\begin{bmatrix}2 & 3 \\ 3 & 7\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 17 & - 7\end{bmatrix}\]
(Every row operation is equivalent to left-multiplication by an elementary matrix.)
 
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Adjoint and Inverse of a Matrix - Exercise 7.3 [पृष्ठ ३६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 7 Adjoint and Inverse of a Matrix
Exercise 7.3 | Q 30 | पृष्ठ ३६

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

The cost of 4 pencils, 3 pens and 2 erasers is Rs. 60. The cost of 2 pencils, 4 pens and 6 erasers is Rs. 90 whereas the cost of 6 pencils, 2 pens, and 3 erasers is Rs. 70. Find the cost of each item by using matrices.


The sum of three numbers is 6. When second number is subtracted from thrice the sum of first and third number, we get number 10. Four times the sum of third number is subtracted from five times the sum of first and second number, the result is 3. Using above information, find these three numbers by matrix method.


Find the inverse of the matrix,  `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.


Solve the following equations by the method of reduction :

2x-y + z=1,  x + 2y +3z = 8, 3x + y-4z=1.


The sum of three numbers is 9. If we multiply third number by 3 and add to the second number, we get 16. By adding the first and the third number and then subtracting twice the second number from this sum, we get 6. Use this information and find the system of linear equations. Hence, find the three numbers using matrices.


If `A=|[2,0,-1],[5,1,0],[0,1,3]|` , then find A-1 using elementary row operations


Using elementary transformations, find the inverse of the matrix A =  `((8,4,3),(2,1,1),(1,2,2))`and use it to solve the following system of linear equations :

8x + 4y + 3z = 19

2xyz = 5

x + 2y + 2z = 7


Using elementary row transformations, find the inverse of the matrix A = `[(1,2,3),(2,5,7),(-2,-4,-5)]`


Prove that :

\[\begin{vmatrix}a & a + b & a + 2b \\ a + 2b & a & a + b \\ a + b & a + 2b & a\end{vmatrix} = 9 \left( a + b \right) b^2\]

 


x + y + z + w = 2
x − 2y + 2z + 2w = − 6
2x + y − 2z + 2w = − 5
3x − y + 3z − 3w = − 3


Use elementary column operation C2 → C2 + 2C1 in the following matrix equation : \[\begin{bmatrix} 2 & 1 \\ 2 & 0\end{bmatrix} = \begin{bmatrix}3 & 1 \\ 2 & 0\end{bmatrix}\begin{bmatrix}1 & 0 \\ - 1 & 1\end{bmatrix}\]


Use elementary column operations  \[C_2 \to C_2 - 2 C_1\] in the matrix equation \[\begin{pmatrix}4 & 2 \\ 3 & 3\end{pmatrix} = \begin{pmatrix}1 & 2 \\ 0 & 3\end{pmatrix}\begin{pmatrix}2 & 0 \\ 1 & 1\end{pmatrix}\] .


If three numbers are added, their sum is 2. If two times the second number is subtracted from the sum of the first and third numbers, we get 8, and if three times the first number is added to the sum of the second and third numbers, we get 4. Find the numbers using matrices. 


Apply the given elementary transformation on each of the following matrices `[(3, -4),(2, 2)]`, R1 ↔ R2.


Apply the given elementary transformation on each of the following matrices `[(3, 1, -1),(1, 3, 1),(-1, 1, 3)]`, 3R2 and C2 ↔ C2 – 4C1.


Find the adjoint of the following matrices : `[(1, -1, 2),(-2, 3, 5),(-2, 0, -1)]`


Choose the correct alternative.

If A = `[("a", 0, 0),(0, "a", 0),(0, 0,"a")]`, then |adj.A| = _______


Choose the correct alternative.

If A = `[(2, 5),(1, 3)]`, then A–1 = _______


Solve the following :

If A = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`, the reduce it to unit matrix by using row transformations.


If three numbers are added, their sum is 2. If 2 times the second number is subtracted from the sum of first and third numbers, we get 8. If three times the first number is added to the sum of second and third numbers, we get 4. Find the numbers using matrices.


Matrix `[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]` is a singular


The suitable elementary row transformation which will reduce the matrix `[(1, 0),(2, 1)]` into identity matrix is ______


If A is a 3 × 3 matrix and |A| = 2, then the matrix represented by A (adj A) is equal to. 


The cofactors of the elements of the first column of the matrix A = `[(2,0,-1),(3,1,2),(-1,1,2)]` are ______.


If `overlinea = 3hati + hatj + 4hatk, overlineb = 2hati - 3hatj + lambdahatk, overlinec = hati + 2hatj - 4hatk` and `overlinea.(overlineb xx overlinec) = 47`, then λ is equal to ______


If A = `[(a, 0, 0), (0, a, 0), (0, 0, a)]`, then the value of |A| |adj A| is ______ 


If AX = B, where A = `[(1, 2, 3), (-1, 1, 2), (1, 2, 4)]` and B = `[(1), (2), (3)]`, then X is equal to ______


If A = `[(1, 1, -1), (1, -2, 1), (2, -1, -3)]`, then (adj A)A = ______


Let F(α) = `[(cosalpha, -sinalpha, 0), (sinalpha, cosalpha, 0), (0, 0, 1)]` where α ∈ R. Then [F(α)]-1 is equal to ______ 


If `[(1, 0, -1),(0, 2, 1),(1, -2, 0)] [(x),(y),(z)] = [(1),(2),(3)]`, then the values of x, y, z respectively are ______.


If `[(2, 3), (3, 1)][(x), (y)] = [(-5), (3)]`, then the values of x and y respectively are ______


If A = `[(1, 2, 1), (3, 2, 3), (2, 1, 2)]`, then `a_11A_11 + a_21A_21 + a_31A_31` = ______ 


The inverse of a symmetric matrix is ______.


In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: The number of elements


Construct a 3 × 2 matrix whose elements are given by aij = ei.x sinjx.


Find the values of a and b if A = B, where A = `[("a" + 4, 3"b"),(8, -6)]`, B = `[(2"a" + 2, "b"^2 + 2),(8, "b"^2 - 5"b")]`


Find the matrix A satisfying the matrix equation:

`[(2, 1),(3, 2)] "A" [(-3, 2),(5, -3)] = [(1, 0),(0, 1)]`


Find A, if `[(4),(1),(3)]` A = `[(-4, 8,4),(-1, 2, 1),(-3, 6, 3)]`


If possible, find BA and AB, where A = `[(2, 1, 2),(1, 2, 4)]`, B = `[(4, 1),(2, 3),(1, 2)]`


Solve for x and y: `x[(2),(1)] + y[(3),(5)] + [(-8),(-11)]` = O


If P = `[(x, 0, 0),(0, y, 0),(0, 0, z)]` and Q = `[("a", 0, 0),(0, "b", 0),(0, 0, "c")]`, prove that PQ = `[(x"a", 0, 0),(0, y"b", 0),(0, 0, z"c")]` = QP


If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (A′)′ = (AB)' = B'A'


If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (kA)' = (kA')


If A = `[(1, 5),(7, 12)]` and B  `[(9, 1),(7, 8)]`, find a matrix C such that 3A + 5B + 2C is a null matrix.


Find the values of a, b, c and d, if `3[("a", "b"),("c", "d")] = [("a", 6),(-1, 2"d")] + [(4, "a" + "b"),("c" + "d", 3)]`


Find x, y, z if A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfies A′ = A–1.


If `[(2x + y, 4x),(5x - 7, 4x)] = [(7, 7y - 13),(y, x + 6)]`, then the value of x + y is ______.


If A = `1/pi [(sin^-1(xpi), tan^-1(x/pi)),(sin^-1(x/pi), cot^-1(pix))]`, B = `1/pi [(-cos^-1(x/pi), tan^-1 (x/pi)),(sin^-1(x/pi),-tan^-1(pix))]`, then A – B is equal to ______.


On using elementary column operations C2 → C2 – 2C1 in the following matrix equation `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`, we have: ______.


In applying one or more row operations while finding A–1 by elementary row operations, we obtain all zeros in one or more, then A–1 ______.


If A = `[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)],` then ____________.


`abs((1,1,1),("e",0,sqrt2),(2,2,2))` is equal to ____________.


If `[(3,0),(0,2)][(x),(y)] = [(3),(2)], "then"  x = 1  "and"  y = -1`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×