Question 4:

\f\f\fConsider the following electrical network - for the numerical values of the voltages and resistan- ces, refer to cells H17- 132 of the Excel file (all voltages are in V, Ill resistances in 12). UA ( Ing Rs RA R6 AAAAAAL Is AAAMA R8 RM R4 RZ Iz R7 Using Ohm's Law and Kirchhoff's Voltage Law, write down a system of Linear equations for the signed current flow intensities In, Iz, Is, Tu, Is in the indicated Flow directions (counter- clockwise around each " small " loop ) . You do not need to solve this system .Consider the Linear transformation T: IR"-IRS, Ly J - T( ( ), given in cells J36-138 of the Excel file. ( a) Find the standard matrix of T. ( b) Find a concrete vector whose image under I is the vector given in cells $43-145 of the Excel file. ( c) Express Ker (T) as a vector span. ( d) Is T injective? Justify your answer. (e) Is I surjective? Justify your answer.Consider the Linear system over IR that is displayed in cells J9- V11 of the Excel file. ( a) Write the augmented matrix of the system (b) Find the general solution of the system, both in parametric and in parametric vector form