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If A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):...

If `A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}]` a=4 and b=-2, then show that (i) (a+b)B=aB+bB (ii) a(C-A)=aC-aA (iii) `(bA)^(T)=bA^(T)`

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Let's solve the given question step by step. Given: - \( A = \begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix} \) - \( B = \begin{pmatrix} 4 & 0 \\ 1 & 5 \end{pmatrix} \) - \( C = \begin{pmatrix} 2 & 0 \\ 1 & -2 \end{pmatrix} \) - \( a = 4 \) - \( b = -2 \) ...
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...

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  2. Show that , if A and B are square matrices such that AB=BA, then (A+B)...

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  3. If A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}] a=4 an...

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  4. If A=[{:(cos q,sin q),(-sin q, cos q):}] , then variefy that A^(2)=[{:...

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  5. If A=[{:( 0,-x),(x,0):}].B=[{:(0,1),(1,0):}] and x^(2)=-1 , then show ...

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  6. Verify that A^(2)=I, when A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}]

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  7. If A is a square matrix, using mathematical induction prove that (A...

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  8. Find inverse, by elementary row operations (if possible) , of both fo...

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  9. If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}], then find the values of x...

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  10. If A=[{:(1,5),(7,12):}] and B=[{:(9,1),( 7,8):}] then find a matrix C ...

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  11. If A=[{:(3,-5),(-1,2):}] then find A^(2)-5A- 4I.

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  12. Find the values of a,b,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,2...

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  13. Find the matrix A such that [{:(2,-1), (1,0),(-3,4):}]A=[{:(-1,-8,-10)...

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  14. If A=[{:(1,2),(4,1):}] , then find A^(2)+2A+7I.

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  15. If A=[{:(cos alpha,sin alpha),(-sin alpha, cos alpha):}] and A^(-1)=A'...

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  16. If matrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is skew-symmetric matrix, the...

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  17. If P(x)=[(cosx, sinx),(-sinx, cosx)], then show that P(x).P(y)=P(x+y)=...

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  18. If A is square matrix such that A^(2)=A, then show that (I+A)^(3)=7A+I...

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  19. If A, B are square matrices of same order and B is skew-symmetric mat...

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

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