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ਦਰਸਾਓ ਕਿ |[a,b,c],[a+2x,b+2y,c+2z],[x,y,...

ਦਰਸਾਓ ਕਿ `|[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]| = 0`

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Without expanding , show that |(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|= 0 .

Using the properties of determinants, show that : |[[x, y, z],[x^2, y^2, z^2],[x,y,z]]|= 0 .

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Using the property of determinants and without expanding , prove that: |[x,a,x+a],[y,b,y+b],[z,c,z+c]| = 0

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Let A= [[a,b,c],[p,q,r],[x,y,z]] and suppose then det (A) = 2, then det (B) equals, where B = [[4x,2a,-p],[4y, 2b, -q],[4z, 2c, -r]]

Find the values of x, y, z if the matrix A = [[0,2y,z],[x,y,-z],[x,-y,z]] satisfy the equation A'A = I

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If [[x+3,z+4,2y-7],[4x+6,a-1,0],[b-3],[3b],[z+2c]] = [[0,6,3y-2],[2x,-3,2c+2],[2b+4],[-2],[0]] , obtain the values of a, b, c, x, y and z.

PSEB-DETERMINANTS-Exercise
  1. ਦਰਸਾਓ ਕਿ |[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]| = 0

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  2. Evaluate the determinant : |[2,4],[-5,-1]|

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  3. Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

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  4. Evaluate the determinant : |[x^2-x+1,x+1],[x+1,x+1]|

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  5. If A = [[1,2],[4,2]], then show that |2A| = 4|A|

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  6. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

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  7. Evaluate the determinant : |[3,-1,-2],[0,0,-1],[3,-5,0]|

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  8. Evaluate the determinant : |[3,-4,5],[1,1,-2],[2,3,1]|

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  9. Evaluate the determinant : |[0,1,2],[-1,0,-3],[-2,3,0]|

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  10. Evaluate the determinant : |[2,-1,-2],[0,2,-1],[3,-5,0]|

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  11. If A = [[1,1,-2],[2,1,-3],[5,4,-9]], find |A|

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  12. Find values of x, if : |[2,4],[5,1]| = |[2x,4],[6,x]|

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  13. Find values of x, if : |[2,3],[4,5]| = |[x,3],[2x,5]|

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  14. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

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  15. Using the property of determinants and without expanding , prove that:...

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  16. Using the property of determinants and without expanding , prove that:...

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  17. Using the property of determinants and without expanding , prove that:...

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  18. Using the property of determinants and without expanding , prove that:...

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  19. Using the property of determinants and without expanding , prove that:...

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  20. Using the property of determinants and without expanding , prove that:...

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  21. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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