(b) Let A and B be 30 × 29 matrices. Show that there exists a vector c E R30 such that both the systems AX = c and BX = c are not soluble. [Hint: consider the two subspaces col(A) and col(B) of R30 and apply part (a).]
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
use results of a to answer b.
![(a) Let S and T be subspaces of a vector space V. Show that SUT is again a
subspace of V if and only if SCT or T C S. Hence show that if S and T
are both proper subspaces of V then SUT +V.
(b) Let A and B be 30 x 29 matrices. Show that there exists a vector c E R30
such that both the systems AX
= c and BX = c are not soluble. [Hint:
consider the two subspaces col(A) and col(B) of R30 and apply part (a).]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c84a4c5-c6b6-4d3a-969f-d3266b05da94%2Fba169df2-d5d3-41e3-a177-487715dda2d0%2F9c3ahkn_processed.png&w=3840&q=75)
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