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Find the product. 3*[[4,-2],[-1,4]]=

Find the product.\newline3⋅[4−2−14]= 3 \cdot\left[\begin{array}{cc}4 & -2 \\ -1 & 4\end{array}\right]=

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Full solution

Q. Find the product.\newline3⋅[4−2−14]= 3 \cdot\left[\begin{array}{cc}4 & -2 \\ -1 & 4\end{array}\right]=
  1. Understand the problem: Understand the problem.\newlineWe need to multiply a scalar (the number 33) by a 2×22 \times 2 matrix ([4−2 −14]\left[\begin{array}{cc}4 & -2 \ -1 & 4\end{array}\right]). This means we will multiply each element of the matrix by the scalar.
  2. Multiply by scalar: Multiply each element of the matrix by the scalar.\newline3×[4−2 −14]=[3×4,3×(−2) 3×(−1),3×4]3 \times \begin{bmatrix} 4 & -2 \ -1 & 4 \end{bmatrix} = \begin{bmatrix} 3\times 4, 3\times (-2) \ 3\times (-1), 3\times 4 \end{bmatrix}
  3. Perform multiplication: Perform the multiplication for each element.\newline\left[\begin{array}{cc}3\times 4, & 3\times (-2)\3\times (-1), & 3\times 4\end{array}\right] = \left[\begin{array}{cc}12, & -6\-3, & 12\end{array}\right]

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