How Well Do You Know Matrices?
If α = [ 1 4 − 6 8 ] and β = [ 2 8 4 3 ] , what is the value of 3 α − 2 β ?
Express your answer as the sum of all elements in the final matrix.
The answer is -13.
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3 solutions
i totally looked at my signs wrong
3 α − 2 β = 3 [ 1 4 − 6 8 ] − 2 [ 2 8 4 3 ] = [ 3 1 2 − 1 8 2 4 ] − [ 4 1 6 8 6 ] = [ 3 − 4 1 2 − 1 6 − 1 8 − 8 2 4 − 6 ] = [ − 1 − 4 − 2 6 1 8 ]
Therefore, the answer required − 1 − 2 6 − 4 + 1 8 = − 1 3 .
Let's multiple 3 for the sum of the elements of the first matrix 3x7 and then subtract the double of the sum of the elements of the second matrix 2×17 21-34=-13
3 α − 2 β = 3 [ 1 4 − 6 8 ] − 2 [ 2 8 4 3 ]
[ 3 1 2 − 1 8 2 4 ] − [ 4 1 6 8 6 ] = [ − 1 − 4 − 2 6 1 8 ]
( − 1 ) + ( − 2 6 ) + ( − 4 ) + 1 8 = − 1 3