मराठी

If a = 0 2 3 − 4 and Ka = 0 3 a 2 B 24 Then Find the Value of K,A and B

Advertisements
Advertisements

प्रश्न

If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.

बेरीज
Advertisements

उत्तर

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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) 65/3/1

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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 x, y, and z from the following equation:

`[(x + y + z), (x + z), (y + z)] = [(9), (5), (7)]`


`A = [a_(ij)]_(m xx n)` is a square matrix, if ______.


Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`


If A = `[(α, β),(γ, -α)]` is such that A2 = I, then ______.


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


if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'


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 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 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:

`[(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")]`


Answer the following question:

If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)]`, B = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, show that AB and BA are both singular matrices


Choose the correct alternative:

If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______


If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______


If A = `[(1, 3, 3),(3, 1, 3),(3, 3, 1)]`, then show that A2 – 5A is a scalar matrix


Show by an example that for A ≠ O, B ≠ O, AB = O


A matrix is said to be a row matrix, if it has


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 = [(1,-1,2),(0,-1,3)], B = [(-2,1),(3,-1),(0,2)],` then AB is a singular matrix.


What is the order of \[A=\begin{bmatrix}0\\ \sqrt{3}\\ -1\\ \dfrac{1}{2}\end{bmatrix}\]?


Which general form represents a row matrix?


What is the order of \[B=\begin{bmatrix}-\dfrac{1}{2}&\sqrt{5}&2&3\end{bmatrix}\]?


What is the order of \[A=\begin{bmatrix}3&-1&0\\ \dfrac{3}{2}&3\sqrt{2}&1\\ 4&3&-1\end{bmatrix}\]?


Which condition holds for a diagonal matrix when \[i\ne j\]?


An identity matrix (unit matrix) is a square matrix with:


How is an identity matrix denoted when its order is \[n\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×