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Math  /  Algebra

QuestionSimplify. −14[12−2028−12]-\frac{1}{4}\left[\begin{array}{ll} 12 & -20 \\ 28 & -12 \end{array}\right]

Studdy Solution

STEP 1

1. We are given a matrix and asked to simplify it by multiplying with a scalar.
2. The scalar multiplication involves multiplying each element of the matrix by the scalar.

STEP 2

1. Multiply each element of the matrix by the scalar −14-\frac{1}{4}.
2. Simplify the resulting elements.

STEP 3

Multiply each element of the matrix by −14-\frac{1}{4}:
−14×[12−2028−12]=[−14×12−14×(−20)−14×28−14×(−12)]-\frac{1}{4} \times \left[\begin{array}{cc} 12 & -20 \\ 28 & -12 \end{array}\right] = \left[\begin{array}{cc} -\frac{1}{4} \times 12 & -\frac{1}{4} \times (-20) \\ -\frac{1}{4} \times 28 & -\frac{1}{4} \times (-12) \end{array}\right]

STEP 4

Simplify each element of the resulting matrix:
[−124204−284124]=[−35−73]\left[\begin{array}{cc} -\frac{12}{4} & \frac{20}{4} \\ -\frac{28}{4} & \frac{12}{4} \end{array}\right] = \left[\begin{array}{cc} -3 & 5 \\ -7 & 3 \end{array}\right]
The simplified matrix is:
[−35−73]\boxed{\left[\begin{array}{cc} -3 & 5 \\ -7 & 3 \end{array}\right]}

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