Multiply the Matrices

Problem

[[1/√(,17),(−4)/√(,17)]]*[[1/√(,17)],[(−4)/√(,17)]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 1×2 row vector and the second is a 2×1 column vector, so the result will be a 1×1 scalar.

2. Apply the dot product formula for matrix multiplication by multiplying corresponding elements and summing them.

(1/√(,17))*(1/√(,17))+((−4)/√(,17))*((−4)/√(,17))

3. Multiply the fractions by multiplying the numerators and denominators.

1/17+16/17

4. Add the resulting fractions.

(1+16)/17

5. Simplify the final fraction.

17/17=1

Final Answer

[[1/√(,17),(−4)/√(,17)]]*[[1/√(,17)],[(−4)/√(,17)]]=1

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