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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 - Mathematics

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प्रश्न

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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उत्तर

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Determinants - Exercise 4.2 [पृष्ठ ११९]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 4 Determinants
Exercise 4.2 | Q 1 | पृष्ठ ११९

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संबंधित प्रश्न

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(A) k|A|

(B) k2 | A |

(C) k3 | A |

(D) 3k | A |


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On expanding by first row, the value of the determinant of 3 × 3 square matrix
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Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. If |A| = 5, write the value of a31 C31  +  a32 C32 a33 C33.


A matrix of order 3 × 3 has determinant 2. What is the value of |A (3I)|, where I is the identity matrix of order 3 × 3.


Which of the following is not correct?


Which of the following is not correct in a given determinant of A, where A = [aij]3×3.


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If x = – 4 is a root of Δ = `|(x, 2, 3),(1, x, 1),(3, 2, x)|` = 0, then find the other two roots.


If x, y ∈ R, then the determinant ∆ = `|(cosx, -sinx, 1),(sinx, cosx, 1),(cos(x + y), -sin(x + y), 0)|` lies in the interval.


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Reason: Determinant A = 0

Which of the following is correct?


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