Advertisements
Advertisements
Question
Find the value of x, y, and z from the following equation:
`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`
Solution
`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`
As the given matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get:
Now, 5 + z = 5 ⇒ z = 0
Also, x + y = 6
y = 6 - x .....(i)
and xy = 8 .....(ii)
Solving (i) & (ii), we have x (6 - x) = 8
= 6x - x2 = 8
x2 - 6x + 8 = 0
= (x - 4) (x - 2) = 0
= x = 2, 4
When x = 2, we get y = 4 and when x = 4, we get y = 6 - 4 = 2
Hence, x = 2, y = 4, z = 0 or x = 4, y = 2, z = 0.
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.
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
Find the value of x, y, and z from the following equation:
`[(4,3),(x,5)] = [(y,z),(1,5)]`
Find the value of a, b, c, and d from the equation:
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB" = B"A. Further, prove that (AB)" = A"B" for all n ∈ N
if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'
Given two matrices A and B
`A = [(1,-2,3),(1,4,1),(1,-3, 2)] and B = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`
find AB and use this result to solve the following system of equations:
x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1
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|.
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`
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 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:
`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
Find k if the following matrix is singular:
`[(7, 3),(-2, "k")]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
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.
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C
State whether the following statement is True or False:
If A is non singular, then |A| = 0
State whether the following statement is True or False:
If `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1
State whether the following statement is True or False:
If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2
The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.
If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.
A square matrix A = [aij]nxn is called a diagonal matrix if aij = 0 for ____________.
If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.
For any square matrix A, AAT is a ____________.
A matrix is said to be a column matrix if it has
If all the elements are zero, then matrix is said to be
How many matrices can be obtained by using one or more numbers from four given numbers?
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 ______.
If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.
A matrix which is both symmetric and skew symmetric matrix is a ______.
