Question

Show that the matrix C=(-2) is a linear combination of the matrices A-(-2 5) v 8=6 6) if so, state the value of the scalars.

68

likes
342 views

Answer to a math question Show that the matrix C=(-2) is a linear combination of the matrices A-(-2 5) v 8=6 6) if so, state the value of the scalars.

Expert avatar
Tiffany
4.5
103 Answers
1. Let's denote the given matrices:
A = \begin{pmatrix}-2 & 5 \\8 & 6\end{pmatrix}, \quad B = \begin{pmatrix}-2\end{pmatrix}, \quad C = \begin{pmatrix}-2\end{pmatrix}

2. We need to find scalars \alpha and \beta such that:
\alpha A + \beta B = C

3. Checking suitable values:
\alpha \begin{pmatrix}-2 & 5 \\8 & 6\end{pmatrix} + \beta \begin{pmatrix}-2\end{pmatrix} = \begin{pmatrix}-2\end{pmatrix}

4. Comparing matrix dimensions and entries, we see that matrix multiplication only affects the element:
0A + 1B = 0 \begin{pmatrix}-2 & 5 \\8 & 6\end{pmatrix} + 1 \begin{pmatrix}-2\end{pmatrix}

5. Thus:
C = 0A + 1B = \begin{pmatrix}-2\end{pmatrix}

Answer:
C = 0A + 1B
with scalars 0 and 1.

Frequently asked questions (FAQs)
What is the limit as x approaches 1 of (x^2 - 1)/(x - 1)?
+
Question: What is the derivative of f(x) = 3x^2 + 5x - 4?
+
What is the product of 17 multiplied by 9?
+
New questions in Mathematics
A=m/2-t isolate t
1 + 1
-6n+5=-13
A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?
Let X be a discrete random variable with range {1, 3, 5} and whose probability function is f(x) = P(X = x). If it is known that P(X = 1) = 0.1 and P(X = 3) = 0.3. What is the value of P(X = 5)?
By differentiating the function f(x)=(x³−6x)⁷ we will obtain
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
(2x+5)^3+(x-3)(x+3)
7/6-(-1/9)
2x+4x=
find f(x) for f'(x)=3x+7
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
A storage maker price is $2.50 per square feet. Find the price of a custom shed 4 yards long, and 5yards wide and 8 feet tall
1. A capital of $3,831 was lent, and it has produced interest of $840 from 05-12-2022 to 1-12-2023. At what annual simple interest rate was the capital lent?
-1%2F2x-4%3D18
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
Find the zero of the linear function 8x + 24 = 0
X^X =49 X=?
A group of 17 people spent 9 days on vacation and spent R$776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?