Use cramer's rule to determine the values of I1,I2,I3 and I4[13.7−4.7−2.20−4.715.40−8.2−2.2025.4−220−8.2−2231.3][I1I2I3I4]=[6−65−9]

Question

Use cramer&#039;s rule to determine the values of I1,I2,I3  and I4[13.7−4.7−2.20−4.715.40−8.2−2.2025.4−220−8.2−2231.3][I1I2I3I4]=[6−65−9]

Benedict · Accepted Answer

Step 1  Given matrices:  A=[13.7−4.7−2.20−4.715.40−8.2−2.2025.4−220−8.2−2231.3],B=[I1I2I3I4],C=[6−65−9]  Multiplication of matrices A and B is possible only when number of columns of matrix A is equal to number of rows of matrix B.  Here order of matrix A is 4×4  and order of matrix B is 4×1 and hence the resultant matrix C has order 4×1  Step 2  Multiplication of matrices:  [13.7−4.7−2.20−4.715.40−8.2−2.2025.4−220−8.2−2231.3][I1I2I3I4]=[6−65−9]  [(13.7)I1−4.7I2−2.2I3+(0)I4−4.7I1+15.4I2+(0)I3−8.2I4−2.2I1+(0)I2+25.4I3−22I4(0)I1−8.2I2−22I3+31.3I4]=[6−65−9]  From the above equation of matrix, four simultaneous equations obtained are:  13.7I1−4.7I2−2.2I3=6  −4.7I1+15.4I2−8.2I4=−6  −2.2I1+25.4I3−22I4=5  −8.2I2−22I3+31.3I4=−9  Solve the above simultaneous equations to get values of unknown variables  I1=0.021  I2=−0.908  I3=−0.655  I4=−0.986

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Use cramer's rule to determine the values of I_1, I_2, I_3 and I_4 begin{bmatrix}13.7 & -4.7 & -2.2 &0 -4.7 & 15.4 & 0 &-8.2 -2.2 & 0 & 25.4 &-22 0 & -8.2 & -22 &31.3 end{bmatrix}begin{bmatrix}I_1 I_2 I_3 I_4 end{bmatrix}=begin{bmatrix}6 -6 5 -9 end{bmatrix}

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