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If A=[2,-1, 3 ,1] and B=[1 ,4 ,7 ,2], fi...

If `A=[2,-1, 3 ,1]` and `B=[1 ,4 ,7 ,2],` find `3A-2Bdot`

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The value of `3A−2B=3[[2,-1],[3,1]]-2[[1,4],[7,2]]`

`=[[6,-3],[9,3]]-[[3,8],[14,4]]`

`=[[6-2,-3-8],[9-14,3-4]]`

`=[[4,-11],[-5,-1]]`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Find a matrix A ,ifA+[2 3 -1 4]=[3 -6 -3 8]

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  2. If A=d i ag(1,-1, 2) and B=d i ag(2 ,3,-1), find A+B ,3A+4Bdot

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  3. If A=[2,-1, 3 ,1] and B=[1 ,4 ,7 ,2], find 3A-2Bdot

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  4. Find the values of a and b if A=B , where A=[[a+4,3b],[8,-6]],B=[[2...

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  5. Find the values of xa n dy if [x+10 y^2+2y0-4]=[3x+4 3 0y^2-5y]

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  6. For what values of x and y are the following matrices equal ? A=[(2x...

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  7. Let A ,B be two matrices such that they commute. Show that for any pos...

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  8. Let A=[[2,3],[-1,2]] and f(x)=x^2 this result of find A^5

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

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  10. If A is a square matrix such that A^2=A , show that (I+A)^3=7A+Idot

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  11. Under what conditions is the matrix A^2-B^2=(A-B)(A+B) is true?

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  12. If a is a non-zero real or complex number. Use the principle of mathe...

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  13. If A = [[cos^2theta, costhetasintheta],[costhetasintheta, sin^2theta]]...

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  14. If A and B are square matrices of order n , then prove that Aa n dB wi...

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  15. Show that positive odd integral powers of a skew-symmetric matrix are ...

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  16. If A=[(costheta,-sintheta),(sintheta,costheta)], then find the values...

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  17. If A=d i ag(abc), show that A^n=d i ag(a^nb^nc^n) for all positive int...

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  18. If A=[[costheta,isintheta],[isintheta,costheta]], then prove by princ...

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  19. Let A=[[1,-1, 0],[ 2, 1, 3],[ 1, 2, 1]] a n d B=[[1 ,2, 3],[ 2, 1, 3],...

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  20. If [xy ,4 , z+6 , x+y]=[8,w,0, 6], write the value of (x+y+z)dot

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