Determine whether the given set s is a subspace of the vector space v.
a. v = m_3 (r) and s is the set of 3 times 3 matrices with trace 0 (recall the trace of a matrix is the sum of its diagonal entries)
b. v = m_3(r) and s is the set of 3 times 3 matrices of rank 1
c. v = m_3 (r) and s is the set of 3 times 3 matrices a such that the vector (7 4 3) is in the of a
d. v = m_2(r) and s is the set of 2 times 2 matrices a such that a^2 = o (here o is the 2 times 2 zero matrix)
e. v = m_2 (r) and s is the set of 2 times 2 matrices that commute with the matrix (0 5 1 6)
f. v = m_3(r) and s is the set of 3 times 3 matrices a such that a^2 = a

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation:

898.1666667

step-by-step explanation:

5389/6 = 898.1666667

no i do not : ( what is it?

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.