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The inverse of matrix is (43, -11, 2).
<h3>What is inverse of matrix?</h3>
A matrix is a multidimensional generalization of the concept of reciprocal of a number: the product between a number and its reciprocal is equal to 1; the product between a square matrix and its inverse is equal to the identity matrix.
given equation:
x + 5y + 10z = 8
y + 4z = -3
x+6y + 15z = 7
The cofactors of the matrix is
C_11 = -9
C_12= 4
C_13=-1
C_21 = -15
C_22= 5
C_23 = -1
C_31= 10
C_32= -4
C_33= 1
The cofactor matrix is,
The transpose of matrix,
The determinant of matrix is = 21.
The augmented matrix is attached below
Hence, the inverse of matrix is (43, -11, 2).
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