If $\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 },$

question 16

Multiple Choice

If $\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 },$ and $X _ { 3 }$ are solutions of the third order system $\mathbf { X } ^ { \prime } = A \mathbf { X }$ and $\mathrm { X } _ { p }$ is a particular solution of $\mathrm { X } ^ { \prime } = A \mathrm { X } + f ( t )$ , then the general solution of $\mathrm { X } ^ { \prime } = A \mathrm { X } + f ( t )$ is

• A) \(c _ { 1 } \mathbf { X } _ { 1 } + c _ { 2 } \mathbf { X } _ { 2 } + c _ { 3 } \mathbf { X } _ { 3 }\)
• B) \(c _ { 1 } \mathbf { X } _ { 1 } + c _ { 2 } \mathbf { X } _ { 2 } + c _ { 3 } \mathbf { X } _ { 3 } + c _ { 4 } \mathbf { X } _ { p }\)
• C) \(c _ { 1 } \mathbf { X } _ { 1 } + c _ { 2 } \mathbf { X } _ { 2 } + c _ { 3 } \mathbf { X } _ { 3 } + \mathbf { X } _ { p }\)
• D) \(\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 3 } + \mathrm { X } _ { p }\)
• E) \(\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 3 } + c _ { 4 } \mathrm { X } _ { p }\)

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Definitions:

Blood Type

The classification of blood based on the presence or absence of specific antigens on the surface of red blood cells, important in blood transfusion and organ transplantation.

Type AB

A blood type in the ABO blood group system that has both A and B antigens on the surface of its red blood cells and is considered the universal plasma donor.

Type B

typically refers to a personality trait characterized by less competitive, more relaxed behaviors as opposed to Type A personality.

Environmental Influence

The impact of surroundings, including physical, biological, and socio-economic factors, on living organisms and their development.