Advertisements
Advertisements
Question
Two matrices are equal if they have same number of rows and same number of columns.
Options
True
False
Solution
This statement is False.
Explanation:
The two matrices are said to be equal if their corresponding elements are same.
APPEARS IN
RELATED QUESTIONS
Find the inverse of the matrix, `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.
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?
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 properties of determinants, prove that :
`|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc + bc + ca + ab`
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.
2x − y = 5
4x − 2y = 7
In the following matrix equation use elementary operation R2 → R2 + R1 and the equation thus obtained:
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.
Transform `[(1, -1, 2),(2, 1, 3),(3, 2, 4)]` into an upper traingular matrix by suitable row transformations.
Find the cofactor matrix, of the following matrices : `[(1, 2),(5, -8)]`
Choose the correct alternative.
If A = `[(2, 5),(1, 3)]`, then A–1 = _______
State whether the following is True or False :
Single element matrix is row as well as column matrix.
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.
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
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 = `[(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 `[(2, 3), (3, 1)][(x), (y)] = [(-5), (3)]`, then the values of x and y respectively are ______
In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: elements a23, a31, a12
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 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)]`
Find A, if `[(4),(1),(3)]` A = `[(-4, 8,4),(-1, 2, 1),(-3, 6, 3)]`
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.
Find the matrix A such that `[(2, -1),(1, 0),(-3, 4)] "A" = [(-1, -8, -10),(1, -2, -5),(9, 22, 15)]`
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 row operation R1 → R1 – 3R2 in the following matrix equation: `[(4, 2),(3, 3)] = [(1, 2),(0, 3)] [(2, 0),(1, 1)]`, 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 ______.
A matrix denotes a number.
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.
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 A = `[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)],` then ____________.
if `A = [(2,5),(1,3)] "then" A^-1` = ______
If `[(3,0),(0,2)][(x),(y)] = [(3),(2)], "then" x = 1 "and" y = -1`
