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प्रश्न
Construct a 3 × 3 matrix whose elements are given by aij = |i – 2j|
उत्तर
aij = |i – 2j|
The general 3 × 3 matrices is
A = `[("a"_11, "a"_12, "a"_13),("a"_21, "a"_22, "a"_23),("a"_31, "a"_32, "a"_33)]`
a11 = |1 – 2(1)| = |1 – 2| = | – 1| = 1
a12 = |1 – 2(2)| = |1 – 4| = | – 3| = 3
a13 = |1 – 2(3)| = |1 – 6| = | – 5| = 5
a21 = |2 – 2(1)| = |2 – 2| = 0 = 0
a22 = |2 – 2(2)| = |2 – 4| = | – 2| = 2
a23 = |2 – 2(3)| = |2 – 6| = | – 4| = 4
a31 = |3 – 2(1)| = |3 – 2| = |1| = 1
a32 = |3 – 2(2)| = |3 – 4| = | – 1| = 1
a33 = |3 – 2(3)| = |3 – 6| = |– 3| = 3
The required matrix A = `[(1, 3, 5),(0, 2, 4),(1, 1, 3)]`
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