Determine the yaluels} of h such that the matrix is the augmented matrix of a consistent linear system. 'lE| E h 5 3 'l Select the correct choice below and, if necessary, ll in the answer box to complete your choice. '3' A- The matrix is the augmented matrix of a consistent linear system if h #D. [Use a comma to separate answers as needed. Type an integer or a simplied fraction]: 0 B- The matrix is the augmented matrix of a consistent linear system if h =|:|. [Use a comma to separate answers as needed. Type an integer or a simplied fraction} CI {2. The matrix is the augmented matrix of a consistent linear system for every yalue of h. C} D. The matrix is not the augmented matrix of a consistent linear system for any value of h. Determine whether the statement below is true er false. Justify the answer. Every elementary new operation is reversible. Cheese the correct answer belew. CI 11. The statement is false. The only reversible rew operation is interchanging two rows. C} B. The statement is true. Replacement, interchanging, and scaling are all reversible. Cl C. The statement is true. lnterchanging can be reversed by scaling, and scaling can be reversed by replacement. C} D. The statement is false. The only reversible new operations are scaling a new and interchanging twe rews. Determine whether the statement below is true or false. Justify the answer. Elementary row operations on an augmented matrix neverchange the solution set of the associated linear system. Choose the correct answer below. O A. The statement is false. Interchanging two rows neverchanges the solution set ofthe associated linear system. However, scaling a row by a nonzero constant can change the solution set of that system. Q B. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found. O C. The statement is true. Each elementary row operation replaces a system with an equivalent system. CI D. The statement is false. Interchanging two rows neverchanges the solution set ofthe associated linear system. However, replacing one row by the sum of itself and a multiple of another row can change the solution set of that system. Determine whether the statement below is true or false. Justify the answer. A 5 x6 matrix has six rows. C Choose the correct answer below. 0 t. The statement is true. A 5 x5 matrix has six columns and six rows. CI B. The statement is true. A 5 x5 matrix has ve columns and six rows. Cl C. The statement is false. A 5 xE- matrix has ve rows and six columns. CI D. The statement is false. A 5 x5 matrix has ve rows and ve columns. Determine whether the statement below is true or false. Justify the answer. Two matrices are row equivalent if they have the same number of rows. Ch oos e CIA." the correct answer below. 'he statement is true. Two matrices are row equivalent if there exists a sequence of elementary row operations that transforms one matrix into the other. 'his can only occur ifthe matrices have the same number of rows. CI B. The statement is false. Two matrices are row equivalent if the equation corresponding to the rst row of the rst matrix is equivalent to the equation corresponding to the rst row of the second matrix, the equation corresponding to the second row of the rst matrix is equivalent to the equation corresponding to the second row of the second matrix, and so forth. 0 C. The statement is true. It is the denition of row equivalence. OD." 'he statement is false. Two matrices are row equivalent if there exists a sequence of elementary row operations that transforms one matrix into the other. Determine whether the statement below is true or false. Justify the answer. Two fundamental questions about a linear system involve existence and uniqueness. Choose the correct answer below. O A. The statement is true. The two fundamental questions are about whetherthe solution exists and whether there is only one solution. C) B. The statement is false. The two fundamental questions are about the type of row operations that can be used on the system and whether the linear operations fundamentally change the system. Cl C. "he statement is true. The two fundamental questions are about whetherthe equations ofthe linear system exist in n-dimensional space and whetherthey can exist in more than one instance of ndimensional space. O D. "he statement is false. The two fundamental questions are about whether it is possible to solve the system with row operations or whether a computer is necessary. Find an equation involving g, h, and k that makes this augmented matrix correspond to a consistent system. 14 59 UBSh 3 47k 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.) 0A. 3ghk=_ OB. 39+h-k=_ Or; 3gh+|-:=_ OD. 39+h+k= \fFind the elementary row operation that transforms the rst matrix into the second, and then nd the reverse operation that transforms the second matrix into the rst. 5 2 5 2 31 -B 53 , -B 53 2 3'l 5 2 5 Find the elementary row operation that transforms the rst matrix into the second. Choose the correct answer below. 0 . Interchange row 2 and row 3. 3- Multiply row'l by D. O C- Multiply row 1 by D and add the result to row 3. O D. Interchange row '1 and row 3. An important concern in the study of heat transfer is to determine the steadystate temperature distribution of a thin plate when the temperature around the boundary is known. The gure represents across 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 ofthe gure. The temperature at a node is approximately equal to the average of the four nearest nodesto the le, above, to the right, and below. Solve the system of equations below to nd the temperatures T1, T4. 41, '2 _ T4=30 -T1+4"2 T3 :70 _ "2+4T3_ T4230 -T1 _ T3+4T4=40 Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. 0 i" "he unique solution ofthe system is (EMBED. [Type integers or decimals rounded to the nearest thousandth as needed} 0 B. "he system has innitely many solutions. O C. "he system has no solution