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 = 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 + z), (x + z), (y + z)] = [(9), (5), (7)]`
If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to ______.
Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3
Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
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.
If\[A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}\]prove that A − AT is a skew-symmetric matrix.
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.
if `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`
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)]`
Find k if the following matrix is singular:
`[(7, 3),(-2, "k")]`
If A = `[(5, 1, -1),(3, 2, 0)]`, Find (AT)T.
Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.
Construct the matrix A = [aij]3 × 3 where aij = i − j. State whether A is symmetric or skew-symmetric.
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
Choose the correct alternative:
If B = `[(6, 3),(-2, "k")]` is singular matrix, then the value of k is ______
State whether the following statement is True or False:
If `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1
If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`
If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.
If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.
`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?
A matrix is said to be a column matrix if it has
A = `[a_(ij)]_(m xx n)` is a square matrix, if
The minimum number of zeros in an upper triangular matrix will be ______.
Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the systems of linear equations (A2B2 – B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has ______.
