I need help with these questions. Thanks

QUESTION 1:

Find an equation involving 9, h, and k that makes this augmented matrix correspond to a consistent system. 13 79 0 3-12h -3 6 -9k a::3 What equation must be satised for the augmented matrix to correspond to a consistent system? Select the correct choice below and ll in the answer box to complete your choice. (Simplify your answer.) {:22- A. 39 + h ' k = (:2:- B. 39 ' h + k = C. 39 + h + k = D. 39 ' h ' k = Find the elementary row operation that transforms the first matrix into the second, and then find the reverse operation that transforms the second matrix into the first. -5 3 5 -5 35 -2 -4 2 2 -20 2 -20 -2 -4 2 . . . Find the elementary row operation that transforms the first matrix into the second. Choose the correct answer below. O A. Interchange row 2 and row 3. O B. Interchange row 1 and row 2. O C. Multiply row 1 by and add the result to row 3. O D. Multiply row 3 byFind the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first. - 2 2 0 - 2 2 0 0 4 - 3 7 0 4 - 3 7 2 - 2 -6 0 3 - 2 -6 . . . Find the elementary row operation that transforms the first matrix into the second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Interchange row 3 and row 2. O B. Replace row 3 by its sum with times row 1. (Type an integer or a simplified fraction.) O C. Replace row 3 by its sum with times row 2. (Type an integer or a simplified fraction.) O D. Scale row 3 by (Type an integer or a simplified fraction.) An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The gure represents a cross section of a metal beam, with negligible heat ow in the direction perpendicular to the plate. Let T1, T4 denote the temperatures at the four interior nodes of the gure. The temperature at a node is approximately equal to the average of the four nearest nodesto the left, above, to the right, and below. Solve the system of equations below to find the temperatures T1, T4. 4T1 T2 - T4 :40 T1 + 4T2 T3 : 65 _ T2 + 4T3 T4 :70 ' T1 T3 + 4T4 : 45 Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. '33:) A- The unique solution of the system is (UNUSED . (Type integers or decimals rounded to the nearest thousandth as needed.) '12:} B. The system has innitely many solutions. '12:} C. The system has no solution