giveny−z=23x+2y+z=45x+4y=1we can write this as0x+y−z=23x+2y+z=45x+4y+0z=1Step 1: Find the determinant of the coefficient matrix.∣∣035124−110∣∣Now find determinant as D=0(2×0−1×4)+1(1×5−3×0)+(−1)(3×4−2×5)=3Step2: Find the determinant of the x− matrix (Dx). X − matrix is formed by replacing the x−column values with the answer−column values∣∣241124−110∣∣Now find determinant =Dx=−21Step3: Find the determinant of the y−matrix (Dy). Y−matrix is formed by replacing the y−column values with the answer−column values∣∣035241−110∣∣Now find determinant =Dy=27Step4: Find the determinant of the z−matrix (Dz). Z−matrix is formed by replacing the z−column values with the answer−column values∣∣035124241∣∣Now find determinant =Dz=21Cramers Rule says that the solutions arex=DDx=3−21=−7y=DDy=327=9z=DDz=321=7
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