For which of the following ordered pairs k,λ,the system of linear equations $$x+2y+3z=k$$,$$3x+4y+5z=4$$,$$4x+4y+4z=$$λis inconsistent

Question

For which of the following ordered pairs k,λ,the system of linear equations $$x+2y+3z=k$$,$$3x+4y+5z=4$$,$$4x+4y+4z=$$λis inconsistent

Infinity Learn · Accepted Answer

Augment matrix $$=$$ $$134$$     $$23k45444$$λapply:$$R2$$→$$R2$$−$$3R1R3$$→$$R3$$−$$4R1$$                                ~$$100$$      $$23k$$−$$2$$−$$44$$−$$3k$$−$$4$$−$$8$$λ−$$4kapply$$:$$R3$$→$$R3$$−$$2R2$$                               ~$$100$$      $$23k$$−$$2$$−$$44$$−$$3k00$$λ$$+2k$$−$$8System$$ is Inconstistant , if λ$$+2k$$−$$8$$≠$$0satisfy$$ by (1$$,$$3) in the given options

For which of the following ordered pairs $(k, λ)$ ,the system of linear equations $x + 2 y + 3 z = k, 3 x + 4 y + 5 z = 4, 4 x + 4 y + 4 z = λ$ is inconsistent

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For which of the following ordered pairs k,λ,the system of linear equations x+2y+3z=k,3x+4y+5z=4,4x+4y+4z=λis inconsistent

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For which of the following ordered pairs $(k, λ)$ ,the system of linear equations $x + 2 y + 3 z = k, 3 x + 4 y + 5 z = 4, 4 x + 4 y + 4 z = λ$ is inconsistent