Advertisements
Advertisements
प्रश्न
If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.
Advertisements
उत्तर
We have, AB = 2I
`|"AB"| = |2"I"|`
⇒ `|"A"| |"B"| = 8`
⇒ `2 |"B"| = 8 ...("Given" |"A"| = 2)`
⇒ `|"B"| = 4`
APPEARS IN
संबंधित प्रश्न
If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.
Find the value of x, y and z from the following equation:
`[(x + y, 2),(5 + z, xy)] = [(6, 2), (5, 8)]`
`A = [a_(ij)]_(m xx n)` is a square matrix, if ______.
if A = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`
if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
Investigate for what values of λ and μ the equations
2x + 3y + 5z = 9
7x + 3y - 2z = 8
2x + 3y + λz = μ have
A. No solutions
B. Unique solutions
C. An infinite number of solutions.
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:
`[9 sqrt(2) -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:
`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]`
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, 0, 1),(0, 1, 0),(1, 0, 0)]`
Identify the following matrix is singular or non-singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
Identify the following matrix is singular or non-singular?
`[(7, 5),(-4, 7)]`
Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
Select the correct option from the given alternatives:
If A and B are square matrices of equal order, then which one is correct among the following?
If A = `[(2, 0, 0),(0, 1, 0),(0, 0, 1)]`, then |adj (A)| = ______
If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
If a matrix A is both symmetric and skew-symmetric, then ____________.
The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.
The matrix A `=[(0,1),(1,0)]` is a ____________.
If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.
`root(3)(4663) + 349` = ? ÷ 21.003
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
The minimum number of zeros in an upper triangular matrix will be ______.
If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.
Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A100B = BA100
Reason: AB = BA implies AB = BA for all positive integers n.
