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Find the product of [(2,3,4),(3,4,5),(4,...

Find the product of `[(2,3,4),(3,4,5),(4,5,6)][(1,-3),(0,2),(3,0)]`

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To find the product of the matrices \(\begin{pmatrix} 2 & 3 & 4 \\ 3 & 4 & 5 \\ 4 & 5 & 6 \end{pmatrix}\) and \(\begin{pmatrix} 1 & -3 \\ 0 & 2 \\ 3 & 0 \end{pmatrix}\), we will follow the matrix multiplication rules. ### Step-by-Step Solution: 1. **Identify the dimensions of the matrices**: - The first matrix \(A\) is a \(3 \times 3\) matrix. - The second matrix \(B\) is a \(3 \times 2\) matrix. - The resulting matrix \(C\) will be of dimension \(3 \times 2\) since the number of columns in \(A\) (3) matches the number of rows in \(B\) (3). ...
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compute the indicated products . (i) [{:(a,b),(-b,a):}][{:(a,-b),(b,a):}](ii) [{:(1),(2),(3):}][2" "3 " "4 ] (iii) [{:(1,-2),(2,3):}][{:(1,2,3),(2,3,1):}] (iv)[{:(2,3,4),(3,4,5),(4,5,6):}][{:(1,-3,5),(0,2,4),(3,0,5):}] (V) [{:(2,1),(3,2),(-1,1):}][{:(1,0,1),(-1,2,1):}] (vi) [{:(3,-1,3),(-1,0,2):}][{:(2,-3),(1,0),(3,1):}]

4) Find the Rank of [[-1,-2,-3],[3,4,5],[4,5,6]]

Find the matrix A such that A.[{:(2,3),(4,5):}]=[{:(0,-4),(10," "3):}].

If the rank of the matrix A= [(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,alpha)] is 3 then a= (A) -5 (B) 5 (C) 4 (D) 4

If A=[(2,3,4),(-3,0,2)], B=[(3,-4,-5),(1,2,1)], C=[(5,-1,0),(7,0,3)], then find A+B+C.

If A={1,2,3},B={3,4}and C={4,5,6}, "then prove that" (AxxB)uu(AxxC) ={(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5 ),(2,6),(3,3),(3,4),(3,5),(3,6)}

show that (i) [{:(5,-1),(6,7):}][{:(2,3),(3,4):}]ne[{:(2,3),(3,4):}][{:(5,-1),(6,7):}] (ii) [{:(1,2,3),(0,1,0),(1,1,0):}][{:(-1,1,0),(0,-1,1),(2,3,4):}] ne[{:(-1,1,0),(0,-1,1),(2,3,4):}][{:(1,2,3),(0,1,0),(1,1,0):}]

Show that (i) [(5,-1),(6,7)][(2,1),(3,4)]!=[(2,1),(3,4)][(5,-1),(6,7)] (ii) [(1,2,3),(0,1,0),(1,1,1)][(-1,1,0),(0,-1,1),(2,3,4)]!=[(-1,1,0),(0,-1,1),(2,3,4)][(1,2,3),(0,1,0),(1,1,0)] .

If A=[(-1,0,2),(3,1,4)], B=[(0,-2,5),(1,-3,1)] and C=[(1,-5,2),(6,0,-4)], then find (2A-3B+4C).

MAHAVEER PUBLICATION-MATRIX-QUESTION BANK
  1. If [(a+b ,2),(5,ab)]=[(6,2),(5,8)], Find the values of a and b.

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  2. Find x,y,a and b if[(2x+3y,a+b,8),(1,4x+y,3a-4b)]=[(7,1,8),(1,9,10)].

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  3. Find the number of all possible matrices of order 3xx3 with each entry...

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  4. Let,A=[(2,4),(3,2)],B=[(1,3),(-2,5)],C[(-2,5),(3,4)] Find each of the ...

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  5. Let,A=[(2,4),(3,2)],B=[(1,3),(-2,5)],C[(-2,5),(3,4)] Find each of the ...

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  6. Let,A=[(2,4),(3,2)],B=[(1,3),(-2,5)],C[(-2,5),(3,4)] Find AB

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  7. Let,A=[(2,4),(3,2)],B=[(1,3),(-2,5)],C[(-2,5),(3,4)] Find BA

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  8. Find the product of [(a,b),(-b,a)][(a,-b),(b,a)]

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  9. Find the product of [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)]

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  10. Find the product of [(2,3,4),(3,4,5),(4,5,6)][(1,-3),(0,2),(3,0)]

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  11. Find X and Y ,ifX+Y =[(7,0),(2,5)] and X-Y= [(3,0),(0,3)]

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  12. Find X and Y ,if 2X + 3Y = [(2,3),(4,0)] and 3X+2Y=[(2,-2),(-1,5)]

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  13. Find ,A^2-5A+6l, ifA = [(2,0,1),(2,1,3),(1,-1,0)].

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  14. Find the transpose of matrices [(1,3,7),(4,2,3)]

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  15. Find the transpose of matrices : [(3),(0),(5)]

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  16. If A^T=[(-2,3),(1,2)] and B =[(-1,0),(1,2)],then find (A +2B)^T.

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  17. Find the value of x if A+A^T=I, where A=[(cos x,- sinx),(sinx, cosx)]...

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  18. If AB are symmetric matrices of same order then show that AB-BA is a s...

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  19. Express matrices as the sum of a symmetric and skew symmetric matrix [...

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  20. Express matrices as the sum of a symmetric and skew symmetric matrix [...

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