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Question

If =∣ ∣ ∣1xx21yy21zz2∣ ∣ ∣ and 1=∣ ∣111yzzxxyxyz∣ ∣, then the value of 1+=

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Solution

Given : 1=∣ ∣111yzzxxyxyz∣ ∣
Taking transpose of above determinant, we get
1=∣ ∣1yzx1zxy1xyz∣ ∣
Now multiplying x in R1,y in R2 and z in R3, we get
1=1xyz∣ ∣ ∣xxyzx2yxyzy2zxyzz2∣ ∣ ∣
1=xyzxyz∣ ∣ ∣x1x2y1y2z1z2∣ ∣ ∣
Now interchanging C1 and C2, we get
1=(1)∣ ∣ ∣1xx21yy21zz2∣ ∣ ∣=
1+=0

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