Explanation Approach: If the system of linear equations is not inconsistent and all the variable in the row-echelon form are not leading variables, then it has infinitely many solutions, and the system is called dependent. If the row echelon form contains a row that represents the equation 0 = c , then the system has no solution. If the system of linear equations has no solutions, then it is inconsistent. Calculation: Consider the system of equations { x + 4 y − 2 z = − 3 2 x − y + 5 z = 12 8 x + 5 y + 11 z = 30 . The augmented matrix is [ 1 4 − 2 − 3 2 − 1 5 12 8 5 11 30 ] . Transform the augmented matrix into row echelon form. Perform the transformation R 2 → R 2 − 2 R 1 . [ 1 4 − 2 − 3 2 − 2 ( 1 ) − 1 − 2 ( 4 ) 5 − 2 ( − 2 ) 12 − 2 ( − 3 ) 8 5 11 30 ] → [ 1 4 − 2 − 3 0 − 9 9 18 8 5 11 30 ] Perform the transformation R 3 → R 3 − 8 R 1 . [ 1 4 − 2 − 3 0 − 9 9 18 8 − 8 ( 1 ) 5 − 8 ( 4 ) 11 − 8 ( − 2 ) 30 − 8 ( − 3 ) ] → [ 1 4 − 2 − 3 0 − 9 9 18 0 − 27 27 54 ] Perform the transformation R 2 → − R 2 9

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Chapter 11.1, Problem 45E

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Whether the system of equation {x+4y−2z=−32x−y+5z=128x+5y+11z=30 is inconsistent or dependent. If dependent, write the complete solution.

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Chapter 11.1, Problem 44E

Chapter 11.1, Problem 46E

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1. Given that h(t) = -5t + 3 t². A tangent line H to the function h(t) passes through the point (-7, B). a. Determine the value of ẞ. b. Derive an expression to represent the gradient of the tangent line H that is passing through the point (-7. B). c. Hence, derive the straight-line equation of the tangent line H 2. The function p(q) has factors of (q − 3) (2q + 5) (q) for the interval -3≤ q≤ 4. a. Derive an expression for the function p(q). b. Determine the stationary point(s) of the function p(q) c. Classify the stationary point(s) from part b. above. d. Identify the local maximum of the function p(q). e. Identify the global minimum for the function p(q). 3. Given that m(q) = -3e-24-169 +9 (-39-7)(-In (30-755 a. State all the possible rules that should be used to differentiate the function m(q). Next to the rule that has been stated, write the expression(s) of the function m(q) for which that rule will be applied. b. Determine the derivative of m(q)

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Chapter 11 Solutions

EBK ALGEBRA AND TRIGONOMETRY

Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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Whether the system of equation { x + 4 y − 2 z = − 3 2 x − y + 5 z = 12 8 x + 5 y + 11 z = 30 is inconsistent or dependent. If dependent, write the complete solution.

Solution Summary: The author analyzes whether the system of equations cx+4y-2z=-3 2x-y+5z = 12 8x +5y +11z

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Whether the system of equation {x+4y−2z=−32x−y+5z=128x+5y+11z=30 is inconsistent or dependent. If dependent, write the complete solution.

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Chapter 11 Solutions