मराठी

If a = ⎡ ⎢ ⎣ 3 9 0 1 8 − 2 7 5 4 ⎤ ⎥ ⎦ and B = ⎡ ⎢ ⎣ 4 0 2 7 1 4 2 2 6 ⎤ ⎥ ⎦ , Then Find the Matrix B ' a ' . - Mathematics

Advertisements
Advertisements

प्रश्न

If A = `[[3,9,0] ,[1,8,-2], [7,5,4]]` and B =`[[4,0,2],[7,1,4],[2,2,6]]` , then find the matrix `B'A'` .

बेरीज

उत्तर

B' = `[[4,7,2],[0,1,2],[2,4,6]]` & A' = `[[3,1,7],[9,8,5],[0,-2,4]]`

`therefore` B'A' = `[[4,7,2],[0,1,2],[2,4,6]][[3,1,7],[9,8,5],[0,-2,4]]`

= `[[12+63,  4+56-4, 28+35+8],[9,8-4,5+8],[6+36,2+32-12,14+20+24]]`

= `[[75,56,71],[9,4,13],[42,22,58]]`

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

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`   

Find AB


Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`

Find BA


Compute the indicated products

`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`


Show that AB ≠ BA in each of the following cases:

`A= [[5    -1],[6        7]]`And B =`[[2       1],[3         4]]`


Compute the products AB and BA whichever exists in each of the following cases:

A = [1 −1 2 3] and B=`[[0],[1],[3],[2]]`

 


If A =

\[\begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\]and B =

\[\begin{bmatrix}- 1 & 3 & 5 \\ 1 & - 3 & - 5 \\ - 1 & 3 & 5\end{bmatrix}\] , show that AB = BA = O3×3.


Let A =`[[-1            1               -1],[3         -3           3],[5           5             5]]`and B =`[[0                4                  3],[1              -3              -3],[-1               4                 4]]`

, compute A2 − B2.

 

If , then show that A is a root of the polynomial f (x) = x3 − 6x2 + 7x + 2.

 

`A=[[1,2,2],[2,1,2],[2,2,1]]`, then prove that A2 − 4A − 5I = 0


Let `A= [[1,1,1],[0,1,1],[0,0,1]]` Use the principle of mathematical introduction to show  that `A^n [[1,n,n(n+1)//2],[0,1,1],[0,0,1]]` for every position integer n.


The cooperative stores of a particular school has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are Rs. 8.30, Rs. 3.45 and Rs. 4.50 each respectively. Find the total amount the store will receive from selling all the items.

 

A trust fund has Rs 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of
(i) Rs 1800 


The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves ₹ 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?


Let  `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that 

(A − B)T = AT − BT


 If \[A = \begin{bmatrix}2 & 4 & - 1 \\ - 1 & 0 & 2\end{bmatrix}, B = \begin{bmatrix}3 & 4 \\ - 1 & 2 \\ 2 & 1\end{bmatrix}\],find `(AB)^T`

 


For the matrices A and B, verify that (AB)T = BT AT, where
\[A = \begin{bmatrix}1 & 3 \\ 2 & 4\end{bmatrix}, B = \begin{bmatrix}1 & 4 \\ 2 & 5\end{bmatrix}\]

If  \[A = \begin{bmatrix}- 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1\end{bmatrix}\] , find A3.

 

 


If  \[\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\begin{bmatrix}3 & 1 \\ 2 & 5\end{bmatrix} = \begin{bmatrix}7 & 11 \\ k & 23\end{bmatrix}\] ,then write the value of k.


If `[2     1       3]([-1,0,-1],[-1,1,0],[0,1,1])([1],[0],[-1])=A` , then write the order of matrix A.


If A and B are two matrices such n  that AB = B and BA = A , `A^2 + B^2` is equal to


The number of possible matrices of order 3 × 3 with each entry 2 or 0 is 


If A is a matrix of order m × n and B is a matrix such that ABT and BTA are both defined, then the order of matrix B is 

Disclaimer: option (a) and (d) both are the same.

 

If A and B are square matrices of the same order, then (A + B)(A − B) is equal to 


Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.


Prove by Mathematical Induction that (A′)n = (An)′, where n ∈ N for any square matrix A.


A matrix which is not a square matrix is called a ______ matrix.


If A = `[(1, 1, 1),(0, 1, 1),(0, 0, 1)]` and M = A + A2 + A3 + .... + A20, then the sum of all the elements of the matrix M is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×