मराठी

Find A, if [413] A = [-484-121-363] - Mathematics

Advertisements
Advertisements

प्रश्न

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

बेरीज

उत्तर

We have, `[(4),(1),(3)]` A = `[(-4, 8,4),(-1, 2, 1),(-3, 6, 3)]`

Let A = `[(x, y, z)]`

∴ `[(4),(1),(3)][(x, y, z)] = [(-4, 8, 4),(-1, 2, 1),(-3, 6, 3)]`

⇒ `[(4x, 4y, 4z),(x, y, z),(3x, 3y, 3z)]  [(-4, 8, 4),(-1, 2, 1),(-3, 6, 3)]`

Comparing elements of both sides

4x = –4

⇒ x = –1

4y = 8

y = 2

and 4z = 4

⇒ z = 1

∴ A = `[(–1, 2, 1)]`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Matrices - Exercise [पृष्ठ ५४]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 3 Matrices
Exercise | Q 13 | पृष्ठ ५४

व्हिडिओ 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.


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.


Express the following equations in the matrix form and solve them by method of reduction :

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


For what values of k, the system of linear equations

x + y + z = 2
2x + y – z = 3
3x + 2y + kz = 4

has a unique solution?

 


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


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


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


2x − 3z + w = 1
x − y + 2w = 1
− 3y + z + w = 1
x + y + z = 1


2x − y = 5
4x − 2y = 7


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

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

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 `[(2, 4),(1, -5)]`, C1 ↔ C2.


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 cofactor matrix, of the following matrices: `[(5, 8, 7),(-1, -2, 1),(-2, 1, 1)]`


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| = _______


Fill in the blank :

Order of matrix `[(2, 1, 1),(5, 1, 8)]` is _______


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


State whether the following statement is True or False:

After applying elementary transformation R1 – 3R2 on matrix `[(3, -2),(1, 4)]` we get `[(0, -12),(1, 4)]`


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


Find the inverse of matrix A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` by using elementary row transformations 


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


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


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


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


If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?


In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: elements a23, a31, a12 


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 non-zero values of x satisfying the matrix equation:

`x[(2x, 2),(3, x)] + 2[(8, 5x),(4, 4x)] = 2[(x^2 + 8, 24),(10, 6x)]`


Find the matrix A satisfying the matrix equation:

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


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


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


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


If `[(xy, 4),(z + 6, x + y)] = [(8, w),(0, 6)]`, then find values of x, y, z and w.


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


If possible, using elementary row transformations, find the inverse of the following matrices

`[(2, -1, 3),(-5, 3, 1),(-3, 2, 3)]`


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: ______.


A matrix denotes a number.


If A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`, then AB and BA are defined and equal.


If `[(2, 0, 7),(0, 1, 0),(1, -2, 1)] [(-x, 14x, 7x),(0, 1, 0),(x, -4x, -2x)] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`then find the value of x


if `A = [(2,5),(1,3)] "then" A^-1` = ______


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×