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Let A=[{:(3,5," "4),(1,2,-3):}]" and "O=...

Let `A=[{:(3,5," "4),(1,2,-3):}]" and "O=[{:(0,0,0),(0,0,0):}]`, then verify that
`A+O=O+A=A.`

Text Solution

Verified by Experts

Clearly, each one of A and O is a matrix of order `(2xx3).`
So, `(A+O)` and `(O+A)` are both defined.
Now, `A+O=[{:(3,5,4),(1,2,-3):}]+[{:(0,0,0),(0,0,0):}]`
`=[{:(3+0,5+0,4+0),(1+0,2+0,-3+0):}]+[{:(3,5,4),(1,2,-3):}]=A.`
And, `O+A=[{:(0,0,0),(0,0,0):}]+[{:(3,5,4),(1,2,-3):}]`
`=[{:(0+3,0+5,0+4),(0+1,0+2,0+(-3)):}]=[{:(3,5,4),(1,2,-3):}]=A.`
Hence, `A+O=O+A=A.`
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RS AGGARWAL-MATRICES-Exercise 5F
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  2. Construct a 2xx3 matrix whose elements are given by a(ij)=(1)/(2)(i-...

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  3. Construct a 2xx3 matrix whose elements are given by a(ij)=(1)/(2)|-3...

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  4. If [{:(x+2y,-y),(3x,4):}]=[{:(-4,3),(6,4):}], find the values of x and...

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  5. Find the values of x and y, if 2[{:(1,3),(0,x):}]+[{:(y,0),(1,2) :}]...

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  6. If x.[{:(2),(3):}]+y.[{:(-1),(1):}]=[{:(10),(5):}], find the values of...

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  7. If [{:(x,3x-y),(2x+z,3y-w):}]=[{:(3,2),(4,7):}], find the values of w...

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  8. If [{:(x,6),(-1,2w):}]+[{:(" "4,x+y),(z+w," "3):}]=3[{:(x,y),(z,w):}],...

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  9. If A=" diag "(3" "-2" "5)" and "B=" diag "(1" "3" "-4)," find "(A+B).

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  10. Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sint...

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  11. If A=[{:(1,-5),(-3," "2),(4,-2):}]" and "B=[{:(3," "1),(2,-1),(-2," "3...

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  12. If A=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}], then find the lea...

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  13. Find the values of x and y for which [{:(2,-3),(1," "1):}][{:(x),(y)...

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  14. Find the values of x and y for which [{:(x,y),(3y,x):}][{:(1),(2):}]...

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  15. If A=[{:(4,5),(1,8):}], show that (A+A') is symmetric.

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  16. If A=[{:(2,3),(4,5):}], show that (A-A') is skew-symmetric.

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  17. If A=[{:(2,-3),(4," "5):}]" and "B=[{:(-1,2),(0,3):}], find a matrix X...

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  18. If A=[{:(4,2),(1,3):}]" and "B=[{:(-2,1),(3,2):}], find a matrix X suc...

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  19. If (i) A=[cosalphasinalpha-sinalphacosalpha] , then verify that Aprime...

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  20. If A and B are two symmetric matrix of same order, then show that (AB-...

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  21. If f(x)=x^2-4x+1 then find f(A) when A=[[2,3] , [1,2]]

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