Advertisements
Advertisements
प्रश्न
Find the value of a, b, c, and d from the equation:
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
उत्तर
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
As the two matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get:
a − b = −1 ....(1)
2a − b = 0 ....(2)
2a + c = 5 ....(3)
3c + d = 13 ...(4)
From (2), we have:
b = 2a
Then, from (1), we have:
a − 2a = −1
⇒ a = 1
⇒ b = 2
Now, from (3), we have:
2 ×1 + c = 5
⇒ c = 3
From (4) we have:
3 ×3 + d = 13
⇒ 9 + d = 13
⇒ d = 4
∴ a = 1, b = 2, c = 3, and d = 4
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 x, y, and z from the following equation:
`[(x+y+z), (x+z), (y+z)] = [(9),(5),(7)]`
if A = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`
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.
If li, mi, ni, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where \[A = \begin{bmatrix}l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3\end{bmatrix}\]
If\[A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}\]prove that A − AT is a skew-symmetric matrix.
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"]`
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:
`[(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:
`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
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, 0, 1),(0, 1, 0),(1, 0, 0)]`
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:
`[(7, 3),(-2, "k")]`
Construct the matrix A = [aij]3 × 3 where aij = i − j. State whether A is symmetric or skew-symmetric.
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A
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
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.
The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.
If A and B are matrices of same order, then (3A –2B)′ is equal to______.
Show by an example that for A ≠ O, B ≠ O, AB = O
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
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 matrix A is both symmetric and skew-symmetric, then ____________.
A diagonal matrix is said to be a scalar matrix if its diagonal elements are
A = `[a_(ij)]_(m xx n)` is a square matrix, if
The number of all possible matrices of order 3/3, with each entry 0 or 1 is
A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.
If the sides a, b, c of ΔABC satisfy the equation 4x3 – 24x2 + 47x – 30 = 0 and `|(a^2, (s - a)^2, (s - a)^2),((s - b)^2, b^2, (s - b)^2),((s - c)^2, (s - c)^2, c^2)| = p^2/q` where p and q are co-prime and s is semiperimeter of ΔABC, then the value of (p – q) is ______.
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 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 ______.
If A is a square matrix of order 3, then |2A| is equal to ______.
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.
