Advertisements
Advertisements
प्रश्न
Find the value of x, y, and z from the following equation:
`[(x + y + z), (x + z), (y + z)] = [(9), (5), (7)]`
Advertisements
उत्तर
`[(x + y + z), (x + z), (y + z)] = [(9), (5), (7)]`
As the two matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get:
x + y + z = 9 ...(1)
x + z = 5 ...(2)
y + z = 7 ...(3)
From (1) and (2), we have:
y + 5 = 9
⇒ y = 4
Then, from (3), we have:
4 + z = 7
⇒ z = 3
∴ x + z = 5
⇒ x = 2
∴ x = 2, y = 4 and z = 3
APPEARS IN
संबंधित प्रश्न
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, 3c + 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 A = `[(α, β),(γ, -α)]` is such that A2 = I, then ______.
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.
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
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|.
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 `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:
`[(0, 4, 7),(-4, 0, -3),(-7, 3, 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:
`[(5),(4),(-3)]`
Identify the following matrix is singular or non-singular?
`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix
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 = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
Choose the correct alternative:
If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______
If A = `[(3, 1),(-1, 2)]`, then prove that A2 – 5A + 7I = O, where I is unit matrix of order 2
If A and B are matrices of same order, then (3A –2B)′ is equal to______.
For the non singular matrix A, (A′)–1 = (A–1)′.
AB = AC ⇒ B = C for any three matrices of same order.
If A is a square matrix, then A – A’ is a ____________.
If a matrix A is both symmetric and skew-symmetric, then ____________.
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
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 ______.
The minimum number of zeros in an upper triangular matrix will be ______.
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 ______.
A matrix which is both symmetric and skew symmetric matrix is a ______.
