Advertisements
Advertisements
Question
`A = [a_(ij)]_(m xx n)` is a square matrix, if ______.
Options
m < n
m > n
m = n
None of these
Advertisements
Solution
`A = [a_(ij)]_(m xx n)` is a square matrix, if m = n.
Explanation:
It is known that a given matrix is said to be a square matrix if the number of rows is equal to the number of columns.
Therefore, `A = [a_(ij)]_(m xx n)` is a square matrix, if m = n.
APPEARS IN
RELATED QUESTIONS
If A is a square matrix, such that A2=A, then write the value of 7A−(I+A)3, where I is an identity matrix.
Find the value of x, y and z from the following equation:
`[(x + y, 2),(5 + z, xy)] = [(6, 2), (5, 8)]`
Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`
If A = `[(α, β),(γ, -α)]` is such that A2 = I, then ______.
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.
If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(3, -2, 4),(0, 0, -5),(0, 0, 0)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(0, 4, 7),(-4, 0, -3),(-7, 3, 0)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(5),(4),(-3)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(6, 0),(0, 6)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix
If A = `[(1, 0),(-1, 7)]`, find k so that A2 – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.
Choose the correct alternative:
If B = `[(6, 3),(-2, "k")]` is singular matrix, then the value of k is ______
The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.
If A and B are matrices of same order, then (3A –2B)′ is equal to______.
For the non singular matrix A, (A′)–1 = (A–1)′.
Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′?
If A is a square matrix, then A – A’ is a ____________.
For any square matrix A, AAT is a ____________.
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
If a matrix A is both symmetric and skew-symmetric, then ____________.
The matrix A `=[(0,1),(1,0)]` is a ____________.
If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.
If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
A = `[a_(ij)]_(m xx n)` is a square matrix, if
A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.
The minimum number of zeros in an upper triangular matrix will be ______.
If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
A matrix which is both symmetric and skew symmetric matrix is a ______.
