[amp_mcq option1=”7a – b – c = 0″ option2=”3a + b – c = 0″ option3=”3a – b + c = 0″ option4=”7a – b + c = 0″ correct=”option1″]<\/p>\n
The correct answer is: A. 7a – b – c = 0<\/p>\n
A system of linear equations is consistent if it has at least one solution. A system of linear equations is said to be dependent if it has infinitely many solutions, and independent if it has exactly one solution.<\/p>\n
To determine whether a system of linear equations is consistent, we can use the following theorem:<\/p>\n
A system of linear equations is consistent if and only if the determinant of the coefficient matrix is not equal to zero.<\/p>\n
In this case, the coefficient matrix is:<\/p>\n
[1 2 -3]
\n[2 3 3]
\n[5 9 -6]<\/p>\n
The determinant of this matrix is:<\/p>\n
7a – b – c<\/p>\n
Therefore, the system of linear equations is consistent if and only if 7a – b – c is not equal to zero.<\/p>\n
Option A: 7a – b – c = 0<\/p>\n
This option satisfies the condition that 7a – b – c is not equal to zero. Therefore, the system of linear equations is consistent.<\/p>\n
Option B: 3a + b – c = 0<\/p>\n
This option does not satisfy the condition that 7a – b – c is not equal to zero. Therefore, the system of linear equations is not consistent.<\/p>\n
Option C: 3a – b + c = 0<\/p>\n
This option does not satisfy the condition that 7a – b – c is not equal to zero. Therefore, the system of linear equations is not consistent.<\/p>\n
Option D: 7a – b + c = 0<\/p>\n
This option does not satisfy the condition that 7a – b – c is not equal to zero. Therefore, the system of linear equations is not consistent.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”7a – b – c = 0″ option2=”3a + b – c = 0″ option3=”3a – b + c = 0″ option4=”7a – b + c = 0″ correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[],"class_list":["post-20011","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"\n