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Write the value of determinant

Answer 1

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Write the value of the determinant : ⎡⎣⎢256x369x4812x⎤⎦⎥[2345686x9x12x]

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A)

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The value of the determinant of a 3×33×3 matrix can be obtained by ⎡⎣⎢a11a21a31a12a22a32a13a23a33⎤⎦⎥[a11a12a13a21a22a23a31a32a33]

If two rows (or columns) are identical,the value of the determinant is 0.

Δ=a11(a22×a33−a23×a32)−a12(a21×a33−a23×a31)+a13(a21×a+32=a22×a31)Δ=a11(a22×a33−a23×a32)−a12(a21×a33−a23×a31)+a13(a21×a+32=a22×a31)

Step 1:

Δ=⎡⎣⎢256x369x4812x⎤⎦⎥Δ=[2345686x9x12x]

Let us take 3x which is the common factor of R3R3,

Δ=⎡⎣⎢252363484⎤⎦⎥Δ=[234568234]

Step 2:

Since two rows are identical the value of the determinant is zero.

Hence Δ=0.

Answer 2

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