Advertisements
Advertisements
प्रश्न
If A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`, then AB and BA are defined and equal.
पर्याय
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`
Since AB is defined
∴ AB = `[(2, 3, -1),(1, 4, 2)] [(2, 3),(4, 5),(2, 1)]`
= `[(4 + 12 - 2, 6 + 15 - 1),(2 + 16 + 4, 3 + 20 + 2)]`
= `[(14, 20),(22, 25)]`
BA is also defined.
∴ BA = `[(2, 3),(4, 5),(2, 1)] [(2, 3, -1),(1, 4, 2)]`
= `[(4 + 3, 6 + 12, -2 + 6),(8 + 5, 12 + 20, -4 + 10),(4 + 1, 6 + 4, -2 + 2)]`
= `[(7, 18, 4),(13, 32, 6),(5, 10, 0)]`
So AB ≠ BA.
APPEARS IN
संबंधित प्रश्न
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.
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
Use elementary column operation C2 → C2 + 2C1 in the following matrix equation :
`[[2,1],[2,0]] = [[3,1],[2,0]] [[1,0],[-1,1]]`
Using the properties of determinants, solve the following for x:
`|[x+2,x+6,x-1],[x+6,x-1,x+2],[x-1,x+2,x+6]|=0`
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
2x + y + z = 5
x + 2y + 2z = 7
The cost of 2 books, 6 notebooks and 3 pens is Rs 40. The cost of 3 books, 4 notebooks and 2 pens is Rs 35, while the cost of 5 books, 7 notebooks and 4 pens is Rs 61. Using this information and matrix method, find the cost of 1 book, 1 notebook and 1 pen separately.
Using elementary row transformations, find the inverse of the matrix A = `[(1,2,3),(2,5,7),(-2,-4,-5)]`
Prove that :
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 + R1 and the equation thus obtained:
Use elementary column operation C2 → C2 + 2C1 in the following matrix equation : \[\begin{bmatrix} 2 & 1 \\ 2 & 0\end{bmatrix} = \begin{bmatrix}3 & 1 \\ 2 & 0\end{bmatrix}\begin{bmatrix}1 & 0 \\ - 1 & 1\end{bmatrix}\]
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.
Using elementary row operations, find the inverse of the matrix A = `((3, 3,4),(2,-3,4),(0,-1,1))` and hence solve the following system of equations : 3x - 3y + 4z = 21, 2x -3y + 4z = 20, -y + z = 5.
Apply the given elementary transformation on each of the following matrices `[(3, -4),(2, 2)]`, R1 ↔ R2.
Find the cofactor matrix, of the following matrices : `[(1, 2),(5, -8)]`
Find the cofactor matrix, of the following matrices: `[(5, 8, 7),(-1, -2, 1),(-2, 1, 1)]`
Find the adjoint of the following matrices : `[(2, -3),(3, 5)]`
Choose the correct alternative.
If A = `[(2, 5),(1, 3)]`, then A–1 = _______
Fill in the blank :
Order of matrix `[(2, 1, 1),(5, 1, 8)]` is _______
Choose the correct alternative:
If A = `[(1, 2),(2, -1)]`, then adj (A) = ______
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)]`
Find the inverse of matrix A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` by using elementary row transformations
For which values of xis the matrix
`[(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)]` non-invertible?
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 ______
If A = `[(1, 1, -1), (1, -2, 1), (2, -1, -3)]`, then (adj A)A = ______
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 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
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 A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (A′)′ = A
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)]`
If P(x) = `[(cosx, sinx),(-sinx, cosx)]`, then show that P(x) . (y) = P(x + y) = P(y) . P(x)
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 possible, using elementary row transformations, find the inverse of the following matrices
`[(2, 3, -3),(-1, 2, 2),(1, 1, -1)]`
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 ______.
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 (AB)′ = B′ A′, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.
`abs((1,1,1),("e",0,sqrt2),(2,2,2))` is equal to ____________.
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` = ______
