Matrices · Question 2

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Let M be a 3 3 matrix such that M bmatrix1\ 0\ 0 bmatrix= bmatrix1\ 2\ 3 bmatrix, M bmatrix0\ 1\ 0 bmatrix= bmatrix0\ 1\ 2 bmatrix and M bmatrix0\ 0\ 1 bmatrix= bmatrix-1\ 1\ 1 bmatrix. If M bmatrixx\ y\ z bmatrix= bmatrix1\ 7\ 11 bmatrix, then x+y+z equals :

Answer

(2) 5

Solution

M multiplied by the unit columns bmatrix1\ 0\ 0 bmatrix, bmatrix0\ 1\ 0 bmatrix, bmatrix0\ 0\ 1 bmatrix gives the 1st, 2nd and 3rd columns of M

M= bmatrix1 & 0 & -1\ 2 & 1 & 1\ 3 & 2 & 1 bmatrix

M bmatrixx\ y\ z bmatrix= bmatrix1\ 7\ 11 bmatrix x-z=1 …(i), 2x+y+z=7 …(ii), 3x+2y+z=11 …(iii)

(iii) − (ii): x+y=4 y=4-x; from (i): z=x-1

in (ii): 2x+(4-x)+(x-1)=7 2x=4 x=2

y=2, z=1

x+y+z=5

Answer: (2)

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