हिंदी

Compute the Products Ab And Ba Whichever Exists in Each of the Following Cases: `A=[[3 2],[-1 0],[-1 0]]` and `B= [[4 5 6],[0 1 2]]` - Mathematics

Advertisements
Advertisements

प्रश्न

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

`A=[[3     2],[-1     0],[-1      1]]` and `B= [[4         5        6],[0           1             2]]`

योग

उत्तर

`AB=[[3        2],[-1       0],[-1     1]]``[[4         5         6],[0       1          2]]`

`⇒AB = [[    12+0                         15+2                      18+4],[-4+0        -5+0       -6+0],[-4+0       -5+1       -6+2]]`

`⇒AB=[[12         17               22],[-4           -5         -6],[-4        -4         -4]]`

Also

`BA=[[4        5       6],[0       1        2]]` `[[3     2],[-1       0],[-1        1]]`

 `⇒BA=[[12-5-6         8+0+6],[0-1-2         0+0+2]]`

`⇒BA=[[1       14],[-3        2]]`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Algebra of Matrices - Exercise 5.3 [पृष्ठ ४१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 5 Algebra of Matrices
Exercise 5.3 | Q 3.2 | पृष्ठ ४१

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Which of the given values of x and y make the following pair of matrices equal?

`[(3x+7, 5),(y+1, 2-3x)] = [(0,y-2),(8,4)]`


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

Find AB


Compute the indicated product.

`[(1),(2),(3)] [2,3,4]`


A trust fund has Rs. 30,000 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. 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of Rs 2,000.


Compute the indicated products:

`[[a    b],[-b      a]][[a     -b],[b         a]]`


Evaluate the following:

`[[1     -1],[0            2],[2           3]]`  `([[1     0        2],[2        0        1]]-[[0             1                 2],[1           0                    2]])`


If A =  `[[4       2],[-1        1]]` 

, prove that (A − 2I) (A − 3I) = O

 

For the following matrices verify the associativity of matrix multiplication i.e. (AB) C = A(BC):

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


Compute the elements a43 and a22 of the matrix:`A=[[0     1        0],[2      0        2],[0       3        2],[4        0       4]]` `[[2       -1],[-3           2],[4              3]]  [[0            1           -1                    2                     -2],[3       -3             4          -4                  0]]`

 


If \[A = \begin{bmatrix}3 & - 5 \\ - 4 & 2\end{bmatrix}\] , find A2 − 5A − 14I.


If A=, find k such that A2 = kA − 2I2

 

Solve the matrix equations:

`[1  2   1] [[1,2,0],[2,0,1],[1,0 ,2]][[0],[2],[x]]=0`


If `A= [[1,2,0],[3,-4,5],[0,-1,3]]` compute A2 − 4A + 3I3.


`A=[[3,2, 0],[1,4,0],[0,0,5]]` show that A2 − 7A + 10I3 = 0


\[A = \begin{bmatrix}\cos \alpha + \sin \alpha & \sqrt{2}\sin \alpha \\ - \sqrt{2}\sin \alpha & \cos \alpha - \sin \alpha\end{bmatrix}\] ,prove that

\[A^n = \begin{bmatrix}\text{cos n α} + \text{sin n α}  & \sqrt{2}\text{sin n  α} \\ - \sqrt{2}\text{sin n α} & \text{cos n α} - \text{sin  n  α} \end{bmatrix}\] for all n ∈ N.

 


If BC are n rowed square matrices and if A = B + CBC = CBC2 = O, then show that for every n ∈ NAn+1 = Bn (B + (n + 1) C).

 

Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?

 

If A and B are square matrices of the same order, explain, why in general

(A + B)2 ≠ A2 + 2AB + B2


Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2 B2? Give reasons.

 

To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:

(i) ₹50       (ii) ₹20       (iii) ₹40

The number of attempts made in three villages XY and Z are given below:

          (i)               (ii)              (iii)
X      400              300             100
Y      300              250               75
Z      500              400             150

Find the total cost incurred by the organisation for three villages separately, using matrices.

 

There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grams of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question?


Let `A= [[1,-1,0],[2,1,3],[1,2,1]]` And `B=[[1,2,3],[2,1,3],[0,1,1]]` Find `A^T,B^T` and verify that   (A + B)T = AT + BT


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

write AB.

 

If A = [aij] is a 2 × 2 matrix such that aij = i + 2j, write A.


If A = [aij] is a square matrix such that aij = i2 − j2, then write whether A is symmetric or skew-symmetric.


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 S = [Sij] is a scalar matrix such that sij = k and A is a square matrix of the same order, then AS = SA = ? 


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


If A is a square matrix such that A2 = I, then (A − I)3 + (A + I)3 − 7A is equal to 


If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find 2X – 3Y


If A = `[(3, 5)]`, B = `[(7, 3)]`, then find a non-zero matrix C such that AC = BC.


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


If AB = BA for any two square matrices, prove by mathematical induction that (AB)n = AnBn 


If matrix A = [aij]2×2, where aij `{:(= 1  "if i" ≠ "j"),(= 0  "if i" = "j"):}` then A2 is equal to ______.


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


If A and B are square matrices of the same order, then (AB)′ = ______.


If A, B and C are square matrices of same order, then AB = AC always implies that B = C


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×