Determine whether the following matrices from M 2,2 form a linearly independent
ID: 1940954 • Letter: D
Question
Determine whether the following matrices from M2,2 form a linearly independent set.
A= 1 -1 4 5 B = 4 3 -2 3 C = 1 -8 22 23Explanation / Answer
If we will be able to express one matrix in terms of others.... then matrix set will form a linearly dependent set. let A = Bx+Cy ; for some real constants x,y if solution for x,y exists.. then linear dependence results else doesnt. =>1 -1 x [ 4 3 y [ 1 -8 4 5 = -2 3] + 22 23 ] =>1 = 4x + y ; -1 = 3x - 8y ; 4 = -2x + 22y ; 5 = 3x + 23y let us solve any two equations.. 4x + y = 1 3x - 8y=-1 solving gives x = 1/5 ; y = 1/5 now substituting in the other equations... the equation 3x+23y = 5 doesnt satisy these values and hence for any linear combination, we will not be able to find a set of constanst satisfying all the equations and hence the given matrices form a linearly independent set .
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