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If A = [[0,6,7],[-6,0,8],[7,-8,0]],B=[[0...

If `A = [[0,6,7],[-6,0,8],[7,-8,0]],B=[[0,1,1],[1,0,2],[1,2,0]],C=[[2],[-2],[3]]` Calculate AC, BC and (A+B)C. Also show that(A+B)C=AC+BC.

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If A=[(0,6,7),(-6,0,8),(7,-8,0)],B=[(0,1,1),(1,0,2),(1,2,0)],C=[(2),(-2),(3)] Calculate AC, BC and (A+B)C . Also, verify that (A+B)C=AC+BC

If A=[(1,1,-1),(2,0,3),(3,-1,2)],B=[(1,3),(0,2),(-1,4)] and C=[(1,2,3,-4),(2,0,-2,1)] , find A(BC), (AB)C and show that (AB)C=A(BC) .

If A = [1,3,4] ,B= [[2,1],[3,7],[6,8]] , C= [[3,4],[5,6],[1,0]] verify that A(B+C) = AB+AC

If A=[(1,2,-3),(5,0,2),(1,-1,1)],B=[(3,-1,2),(4,2,5),(2,0,3)] and C=[(4,1,2),(0,3,2),(1,-2,3)] , then compute (A+B) and (B-C) . Also, verify that A+(B-C)=(A+B)-C .

If A={:[(2,0,9),(-1,6,10),(4,-1,2)]:},B={:[(0,-1,-2),(3,2,-1),(4,-2,0)]:} and C={:[(1,-2,0),(0,1,2),(3,0,-1)]:} then show that, A(B+C) = AB + AC.

If A={:[(2,0,9),(-1,6,10),(4,-1,2)]:},B={:[(0,-1,-2),(3,2,-1),(4,-2,0)]:} and C={:[(1,-2,0),(0,1,2),(3,0,-1)]:} then show that, A(BC) = (AB)C

Let A +2B=[[1, 2, 0],[ 6,-3, 3],[-5, 3, 1] ] and 2A-B=[[2,-1, 5 ],[2,-1, 6],[ 0, 1, 2]] . Then T r(B) has the value equal to a. 0 b. 1 c. 2 d. none

If A={:[(2,-3),(0,1),(-1,4)],B={:[(-1,5),(2,-3),(0,1)],C={:[(4,-2),(0,-1),(3,5)], Find the matrices A + 4B - 3C

If A={:[(1,-2,2),(0,1,-1),(0,0,1)]:} and B={:[(1,2,0),(2,3,-1),(0,-1,-2)]:}, then show that, (A'B)A is a diagonal matrix.

If A={:[(2,-3),(0,1),(-1,4)],B={:[(-1,5),(2,-3),(0,1)],C={:[(4,-2),(0,-1),(3,5)], Find the matrices 2B - 3C

UNITED BOOK HOUSE-HIGHER SECONDARY EXAMINATION 2020.-EXERCISE
  1. *' is an operation defined on Z set of all integers as a*b = a+b-2 for...

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  2. Show that sin^(-1) (12/13)+cos^(-1)(4/5)+tan^(-1)(63/16) = pi.

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  3. If A = [[0,6,7],[-6,0,8],[7,-8,0]],B=[[0,1,1],[1,0,2],[1,2,0]],C=[[2],...

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  4. If A = ([cos theta,sin theta],[-sin theta,cos theta]) show that A= ([c...

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  5. show that |[1,x,x^2],[x^2,1,x],[x,x^2,1]| = (1-x^3)^2

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  6. If (cos x)^y = (cos y)^x then show that (dy)/(dx) = (y tan x+log cos y...

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  7. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

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  8. Evaluate: int(2dx)/((1-x)(1+x^2))

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  9. Evaluate: int (sqrt(tanx)+sqrtcotx)dx

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  10. Solve: xy (dy)/(dx)=(x+2)(y+2), given x= 1, when y =-1.

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  11. Solve: x^2dy+(xy+y^2)dx=0, given x=1 and y = 1.

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  12. If vec a,vec b, vec c be three vectors such that vec a+vec b+vec c=0 ,...

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  13. Show that the points A=(2,-1,1),B=(1,-3,-5) and C=(3,-4,-4) are verti...

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  14. Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2.

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  15. Let A and B be two events such that P(A) =1/3,P(B)=1/4 and P(AnnB)=1/4...

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  16. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

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  17. Solve: (dy)/(dx)-3ycot x=sin2x, given y=2 when x= pi/2

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  18. Find two positive numbers x and y such that x + y = 60 and xy^(3) is m...

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  19. Evaluate the following integral overset(3)underset(1)int (x^2+x)dx.

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  20. A variable plane which is at a constant distance 3p from origin cuts t...

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