Advertisements
Advertisements
प्रश्न
Find the value of x, y, and z from the following equation:
`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`
Advertisements
उत्तर
`[(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
संबंधित प्रश्न
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |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.
A coaching institute of English (subject) conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, it has 20 poor and 5 rich children and total monthly collection is Rs 9,000, whereas in batch II, it has 5 poor and 25 rich children and total monthly collection is Rs 26,000. Using matrix method, find monthly fees paid by each child of two types. What values the coaching institute is inculcating in the society?
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\[A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}\]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 `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"]`
Choose the correct alternative.
The matrix `[(8, 0, 0),(0, 8, 0),(0, 0, 8)]` is _______
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:
`[(3, 0, 0),(0, 5, 0),(0, 0, 1/3)]`
Identify the following matrix is singular or non-singular?
`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`
Identify the following matrix is singular or non-singular?
`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`
Find k if the following matrix is singular:
`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
If A = `[(5, 1, -1),(3, 2, 0)]`, Find (AT)T.
Construct the matrix A = [aij]3 × 3 where aij = i − j. State whether A is symmetric or skew-symmetric.
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.
If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is unit matrix of order 2
If A = `[(1, 3, 3),(3, 1, 3),(3, 3, 1)]`, then show that A2 – 5A is a scalar matrix
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 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 ____________.
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.
The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.
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 ____________.
If a matrix A is both symmetric and skew symmetric then matrix A is ____________.
A matrix is said to be a column 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 D = `[(0, aα^2, aβ^2),(bα + c, 0, aγ^2),(bβ + c, (bγ + c), 0)]` is a skew-symmetric matrix (where α, β, γ are distinct) and the value of `|((a + 1)^2, (1 - a), (2 - c)),((3 + c), (b + 2)^2, (b + 1)^2),((3 - b)^2, b^2, (c + 3))|` is λ then the value of |10λ| is ______.
If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.
Let A = `[(0, -2),(2, 0)]`. If M and N are two matrices given by M = `sum_(k = 1)^10 A^(2k)` and N = `sum_(k = 1)^10 A^(2k - 1)` then MN2 is ______.
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.
