#453easyMatrix Operations

2x2 Matrix Multiplication

Time Limit: 2sMemory: 256MB

Problem

Given two $2 \times 2$ matrices $A$ and $B$ , compute their product $C = AB$ .

$C_{ij} = \sum_{k=1}^{2} A_{ik} B_{kj}$

For 2x2 matrices, this expands to four entries, each being a dot product of a row of $A$ with a column of $B$ .

Eight space-separated values: a11 a12 a21 a22 b11 b12 b21 b22

(Matrix $A$ in row-major order, then matrix $B$ in row-major order.)

Four space-separated values: c11 c12 c21 c22, each to 4 decimal places.

Example 1

Input(Eight space-separated values: a11 a12 a21 a22 b11 b12 b21 b22)

1 2 3 4 5 6 7 8

Output

19.0000 22.0000 43.0000 50.0000

A=[[1,2],[3,4]] * B=[[5,6],[7,8]] = [[19,22],[43,50]].

Example 2

Input(Eight space-separated values: a11 a12 a21 a22 b11 b12 b21 b22)

1 0 0 1 3 4 5 6

Output

3.0000 4.0000 5.0000 6.0000

Identity times B equals B.

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