Advertisements
Advertisements
Question
Let A = `((2,-1),(3,4))`, B = `((5,2),(7,4))`, C= `((2,5),(3,8))` find a matrix D such that CD − AB = O
Advertisements
Solution
Since A, B and C are all square matrices or order 2 and CD − AB is well defined, D must be a square matrix of order 2.
Let D = `[(a,b),(c,d)]`
Then CD − AB = O gives,
`[(2,5),(3,8)][(a,b),(c,d)] - [(2,-1),(3,4)][(5,2),(7,4)] = O`
`=>[(2a + 5c,2b+5a),(3a+8c, 3b+8a)]-[(3,0),(43,22)] = [(0,0),(0,0)]`
`=>[(2a + 5c - 3, 2b + 5d),(3a + 8c - 43, 3b + 8d - 22)] = [(0,0),(0,0)]`
By equality of matrices we get,
2a + 5c − 3 = 0 ...(1)
3a + 8c − 43 = 0 ...(2)
2b + 5d = 0 ...(3)
3b + 8d − 22 = 0 ...(4)
By solving (1) and (2) we get a = −191 and c = 77.
Similarly, on solving (3) and (4) we get b = - 110 and d = 44.
Therefore,
`D = [(a,b),(c,d)] = [(-191,-110),(77,44)]`
APPEARS IN
RELATED QUESTIONS
If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to ______.
Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.
Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`
In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
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:
`[(6, 0),(0, 6)]`
Answer the following question:
If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.
Answer the following question:
If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
If A = `[(2, 0, 0),(0, 1, 0),(0, 0, 1)]`, then |adj (A)| = ______
If A = `[(3, 1),(-1, 2)]`, then prove that A2 – 5A + 7I = O, where I is unit matrix of order 2
For the non singular matrix A, (A′)–1 = (A–1)′.
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.
A matrix is said to be a row matrix, if it has
A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
If all the elements are zero, then matrix is said to be
A = `[a_(ij)]_(m xx n)` is a square matrix, if
A matrix with only one row is called a:
Which condition holds for a diagonal matrix when \[i\ne j\]?
A scalar matrix is a diagonal matrix in which:
Which matrix is a scalar matrix?
Which matrix is an identity matrix?
What is the notation for a zero matrix?
