Math Problem Statement
Do the following matrix operations WITHOUT USING YOUR CALCULATORS: (i) 4A, (ii) A + C, (iii) 3B + 2C, (iv) 2A - C + 4B where A = [[2, -3], [-1, 6]], B = [[4, 1], [-5, 2]], C = [[-3, 5], [4, -2]]
Solution
Let's break down and solve the matrix operations one by one from the image:
The matrices are:
(i)
To find , we multiply every element of matrix by 4:
= \begin{bmatrix} 4 \times 2 & 4 \times (-3) \\ 4 \times (-1) & 4 \times 6 \end{bmatrix} = \begin{bmatrix} 8 & -12 \\ -4 & 24 \end{bmatrix}$$ ### (ii) $$A + C$$ To add matrices $$A$$ and $$C$$, we simply add corresponding elements: $$A + C = \begin{bmatrix} 2 & -3 \\ -1 & 6 \end{bmatrix} + \begin{bmatrix} -3 & 5 \\ 4 & -2 \end{bmatrix} = \begin{bmatrix} 2 + (-3) & -3 + 5 \\ -1 + 4 & 6 + (-2) \end{bmatrix} = \begin{bmatrix} -1 & 2 \\ 3 & 4 \end{bmatrix}$$ ### (iii) $$3B + 2C$$ For this, we first compute $$3B$$ and $$2C$$, then add them. $$3B = 3 \times \begin{bmatrix} 4 & 1 \\ -5 & 2 \end{bmatrix} = \begin{bmatrix} 12 & 3 \\ -15 & 6 \end{bmatrix}$$ $$2C = 2 \times \begin{bmatrix} -3 & 5 \\ 4 & -2 \end{bmatrix} = \begin{bmatrix} -6 & 10 \\ 8 & -4 \end{bmatrix}$$ Now, add $$3B$$ and $$2C$$: \[ 3BAsk a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Multiplication
Matrix Addition
Scalar Multiplication
Formulas
Matrix Multiplication: cA = c * [[a, b], [d, e]] = [[c * a, c * b], [c * d, c * e]]
Matrix Addition: A + B = [[a1 + b1, a2 + b2], [c1 + c2, d1 + d2]]
Theorems
Matrix Algebra
Suitable Grade Level
Undergraduate Level (Introductory Linear Algebra)