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Asked by sharmasaumya453 | 16 Sep, 2020, 03:07: PM
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Question: Let M be a 3x3 matrix satisfying M[0 // 1 // 0] = [-1 // 2 // 3], M[1 // -1 // 0] = [1 // 1 // -1] and M[1 // 1 // 1] = [0 // 0 // 12]. Then the sum of diagonals of M is
Solution:
Take matrix M as [m11 m12 m13 // m21 m22 m23 // m31 m32 m33]
Taking M[0 // 1 // 0] = [-1 // 2 // 3] we get m12 = -1, m22 = 2 and m32 = 3 ... (i)
Taking M[1 // -1 // 0] = [1 // 1 // -1] we get m11 - m12 = 1, m21 - m22 = 1 and m31 - m32 = -1
Substituting the values obtained in (i), we get
m11 = 0, m21 = 3 and m31 = 2
Similarly, we get m13 = 1, m23 = -5 and m33 = 7
Hence, the sum of diagonals = m11 + m22 + m33 = 0 + 2 + 7 = 9
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