If A=[{:(2, 1,),(4,2,)],B =[{:(2,3,4),(1...

If `A=[{:(2, 1,),(4,2,)],B =[{:(2,3,4),(1,4,0):}]` and `C=[{:(-1,2,1),(1,0,2):}]` then veri fy that `A(B+C)=(AB+AC)`.

Text Solution

AI Generated Solution

To verify that \( A(B+C) = AB + AC \) for the given matrices \( A \), \( B \), and \( C \), we will follow these steps: ### Step 1: Define the Matrices Given: \[ A = \begin{pmatrix} 2 & 1 \\ 4 & 2 \end{pmatrix}, \quad B = \begin{pmatrix} 2 & 3 & 4 \\ 1 & 4 & 0 \end{pmatrix}, \quad C = \begin{pmatrix} -1 & 2 & 1 \\ 1 & 0 & 2 \end{pmatrix} \] ...

Topper's Solved these Questions

LINEAR PROGRAMMING
NCERT EXEMPLAR ENGLISH|Exercise TRUE/FALSE|2 Videos
PROBABILITY
NCERT EXEMPLAR ENGLISH|Exercise True/False|9 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(,2,1),(,0,0):}], B=[{:(,2,3),(,4,1):}] and C=[{:(,1,4),(,0,2):}] then show that (i) A(B+C)=AB+AC (ii) (B-A)C=BC-AC .

If A=[{:(,1,4),(,2,1):}], B=[{:(,-3,2),(,4,0):}] and C=[{:(,1,0),(,0,2):}] simplify : A^2+BC .

If A[{:(3,-4),(1,1),(2,0):}] and B=[{:(2,1,2),(1,2,4):}] and B=[{:(4,1),(2,3),(1,2):}]

If A=[{:(1,2),(-2,1):}],B=[{:(2,3),(3,-4):}] and C=[{:(1,0),(-1,0):}] , verfity (i) A(B+C)=AB+AC.

If A = [{:(1,2),(-2,3):}], B= [{:(2,1),(2,3):}] and C = [{:(-3,1),(2,0):}] ,verify that (AB)C = A(BC) and A(B+C)=AB+AC.

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

If A=[{:(,1,3),(,2,4):}], B=[{:(,1,2),(,4,3):}] and C=[{:(,4,3),(,1,2):}] . Find (i) (AB) C (ii) A (BC) Is A(BC)=(AB) C?

if A=[{:(4,0,-3),(1,2,0):}]and B=[{:(2,1),(1,-2),(3,4):}]' then find AB and BA.

if A=[{:(2,-3),(1,4):}],B=[{:(-1,0),(1,2):}], C=[{:(3,1),(1,2):}] , then show that A (BC)=(AB)c.

If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify that (i) (A')'=A (ii) (AB)'=B'A'

NCERT EXEMPLAR ENGLISH-MATRICES-Solved example

If P=[x0 0 0y0 0 0z] and Q=[a0 0 0b0 0 0c] , prove that P Q=[x a0 0 0y...
Text Solution
|
If [2 1 3] [{:(-1,0,-1),(-1,1,0),(0,1,1):}][{:(1),(0),(-1):}]=A, then ...
Text Solution
|
If A=[{:(2, 1,),(4,2,)],B =[{:(2,3,4),(1,4,0):}] and C=[{:(-1,2,1),(1,...
Text Solution
|
If A=[{:(1,0,-1),(2,1,3),(0,1, 1):}] then verify that A^(2)+A=A(A+I) ,...
Text Solution
|
If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify...
Text Solution
|
If A=[{:(1,2),(4,1),(5,6):}] and B=[{:(1,2),(6,4),(7,3):}], then varif...
Text Solution
|
Show that A' A and A A' are both symmetric matrices for any matrix A.
Text Solution
|
Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...
Text Solution
|
Show that , if A and B are square matrices such that AB=BA, then (A+B)...
Text Solution
|
If A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}] a=4 an...
Text Solution
|
If A=[{:(cos q,sin q),(-sin q, cos q):}] , then variefy that A^(2)=[{:...
Text Solution
|
If A=[{:( 0,-x),(x,0):}].B=[{:(0,1),(1,0):}] and x^(2)=-1 , then show ...
Text Solution
|
Verify that A^(2)=I, when A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}]
Text Solution
|
If A is a square matrix, using mathematical induction prove that (A...
Text Solution
|
Find inverse, by elementary row operations (if possible) , of both fo...
Text Solution
|
If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}], then find the values of x...
Text Solution
|
If A=[{:(1,5),(7,12):}] and B=[{:(9,1),( 7,8):}] then find a matrix C ...
Text Solution
|
If A=[{:(3,-5),(-1,2):}] then find A^(2)-5A- 4I.
Text Solution
|
Find the values of a,b,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,2...
Text Solution
|
Find the matrix A such that [{:(2,-1), (1,0),(-3,4):}]A=[{:(-1,-8,-10)...
Text Solution
|