Advertisements
Advertisements
Question
If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.
Advertisements
Solution
Given,
kA = `[[0 , 3"a"],[2"b", 24]]` .....(i)
A = `[[0 , 2],[3, -4]]`, implies kA = `[[0 , 2"k"],[3"k", -4"k"]]` .....(ii)
`[[0 , 2"k"],[3"k", -4"k"]] = [[0, 3"a"],[2"b" , 24]]`
- 4k = 24 ⇒ k = - 6
3a = 2k ⇒ a = - 4
2b = 3k ⇒ b = - 9
APPEARS IN
RELATED QUESTIONS
Find the value of x, y and z from the following equation:
`[(4, 3),(x, 5)] = [(y, z),(1, 5)]`
If A = `[(0, -tan α/2), (tan α/2, 0)]` and I is the identity matrix of order 2, show that I + A = `(I - A)[(cos α, -sin α),(sin α, cos α)]`
Let A = `[(0,1),(0,0)]`show that (aI+bA)n = anI + nan-1 bA , where I is the identity matrix of order 2 and n ∈ N
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
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
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:
`[(6, 0),(0, 6)]`
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)]`
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)]`
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:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
If A = `[(2, 0, 0),(0, 1, 0),(0, 0, 1)]`, then |adj (A)| = ______
If two matrices A and B are of the same order, then 2A + B = B + 2A.
If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.
If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.
If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.
If a matrix A is both symmetric and skew symmetric then matrix A is ____________.
If all the elements are zero, then matrix is said to be
Let A be a 2 × 2 real matrix with entries from {0, 1} and |A| ≠ 0. Consider the following two statements:
(P) If A1I2, then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,
where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then ______.
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 ______.
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 ______.
What is the order of a column matrix with \[m\] rows?
What is the order of a row matrix with \[n\] columns?
What is the order of \[B=\begin{bmatrix}-\dfrac{1}{2}&\sqrt{5}&2&3\end{bmatrix}\]?
A matrix where the number of rows equals the number of columns is called a:
If \[m=n\], what type and order does the matrix have?
Which elements can be non-zero in a diagonal matrix?
A scalar matrix is a diagonal matrix in which:
Which matrix is an identity matrix?
Which matrix is a zero matrix?
