Name September 252, 2017 M 250/ M 314 - LINEAR ALGEBRA TEST, 1 #1. Solve the fol

Question

Name September 252, 2017 M 250/ M 314 - LINEAR ALGEBRA TEST, 1 #1. Solve the following linear systems by Gaus,Jordan reduction: 2. Consider the system of equations z+2y + 3z = 4 where k is a constant. (a) For which values of k does the system have infinltely many solutions? (b) For which values of k does the system have a unique solution? (e) For which values of k does the system have no solution? #3. Express the vector (s) as the sum of a vector on the line y-3r and a vector on the liney #4. For which values of the constant c is the vector ( c ) ? a linearoombination of and #5. Let Compute the following (a) A7, (b) A01, 6, Find all matrices X that satisfy the following matrix equation

Explanation / Answer

3) a(y-3x)+b(y-x)=x+5y

a+b=5 and -3a-b=1

-2a=6=>a=-3 ,b=8

4) a+b=1 ,2a+3b=c,4a+9b=c2

   from equation 2 we get 2+b=c

(2+b)2 = 4(1-b)+9b

4+4b+b2=4-4b+9b

=>b=1,a=0

a times first vector + b times second vector is given result

5)A power even will give 1 0

                                         0   1

A power odd will give A

so a)answer is A

b)answer is 1    0

                    0   -1

6)2x3 * 3x2 matrix will give 2x2 matrix

let X be a1 b1

              a2   b2

              a3 b3

a1+2*a2+3*a3 = 0 and a2 + 2*a3 =0

a1=a3,b1=b3

a2=-2*a3,b2=-2*b3

X should be of form a   b

                               -2a -2b

                                 a     b

where a,b are constants

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