The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r r } 1 & 4 & - 2 & - 3 & 1 \\0 & 0 & 1 & 4 & - 4 \\- 1 & - 4 & 0 & - 5 & 7\end{array} \right]$$

question 38

Multiple Choice

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.
- $$\left[ \begin{array} { r r r r r } 1 & 4 & - 2 & - 3 & 1 \\0 & 0 & 1 & 4 & - 4 \\- 1 & - 4 & 0 & - 5 & 7\end{array} \right]$$

• A) \(x _ { 1 } = - 4 x _ { 2 } + 2 x _ { 3 } + 3 x _ { 4 } + 1\)
• \(x _ { 2 }\) is free
• \(x _ { 3 } = - 4 - 4 x _ { 4 }\)
• \(x _ { 4 }\) is free
• B) \(\times _ { 1 } = - 7 - 4 \times _ { 2 } - 5 x _ { 4 }\)
• \(x _ { 2 }\) is free
• \(x _ { 3 } = - 4 - 4 x _ { 4 }\)
• \(x _ { 4 }\) is free
• C) \(x _ { 1 } = - 7 - 4 x _ { 2 } - 5 x _ { 4 }\)
• \(x _ { 2 }\) is free
• \(x _ { 3 } = - 4 - 4 x _ { 4 }\)
• \(x _ { 4 } = 0\)
• D) \(x _ { 1 } = - 7 - 4 x _ { 2 } - 5 \times 3\)
• \(x _ { 2 } = - 4 - 4 x _ { 3 }\)
• \(x _ { 3 }\) is free

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Definitions:

Chorion

The outermost fetal membrane in mammals, including humans, contributing to the formation of the placenta.

Ectopic Pregnancy

A pregnancy in which the fertilized egg implants outside the uterus, often in the fallopian tube, and is non-viable.

Embryo Transfer

A step in assisted reproduction where an embryo is placed into the uterus of a female with the intent of establishing a pregnancy.

Preembryonic Development

The earliest phase of human development, from fertilization to the formation of the embryonic disc, which is before the actual embryo begins to form.