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 volume of a cone with radius 5cm and height 8cm?
+
What is the value of sine of x if the cosine of x is 0.7?
+
Math Question: In triangle ABC, angle A measures 60 degrees. If the angle bisector of A intersects side BC at point D, and side BC measures 10 units, what is the length of BD?
+
New questions in Mathematics
Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?
A=m/2-t isolate t
(x^2+3x)/(x^2-9)=
Determine all solutions to the inequality |2x + 6| − |x + 1| < 6. Write your final answer in interval notation
³√12 x ⁶√96
two pails of different sizes contain 34.5 litres of water altogether When 0.68 litre of water is poured from the bigger pail into the smaller pail the amount of water in the bigger pail is 9 times that in the smaller pail. How much water was in the smaller pail at first?
solve the following trigo equation for 0°<= x <= 360°. sec x =-2
4X^2 25
We have spent 1/4 of the inheritance on taxes and 3/5 of the rest on buying a house. If the inheritance was a total of €150,000 How much money do we have left?
The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. a) What is the amount of VAT paid by the hotel for one
DuocUC 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function: (x+185) C(x)=81300-6x+ 20000 a) It is known that C(90) 5.344. Interpret this result. (2 points) b) Calculate C'(x) (2 points) 3 x²+111x-0.87 20000 2000 c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing. (3 points) d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost? (
List the remaining zeros of the polynomial with the given zeros Zeros are: 2, 3i, and 3 + i
9/14 x 7/27 carry out indicated operation
A house located within the city limits has a current market value of $325,000 according to a recent appraisal. The assessed value from the last county wide tax valuation is $272,475. The tax rate is $0.36 per hundred for the county and $0.72 per hundred for the city. What is the total annual property tax liability on the property? $2340 $3510 $1962 $2943
Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)
Consider mixing 150 ml, 0.1M, HCI with 100 ml, 0.2M, KOH solution. Determine the pH of final solution.
Perform operations with the polynomials P(x) = x3 and Q(x) = 2x2 + x – 3x3 : a) P(x) - Q(x)
there are 500,000 bacteria at the end of a pin point. 1000 bacteria can make a person sick. then bacteria at the tip of a pin point can make 500 people sick. Also, many people do not know that bacteria can (reproduce). Let's say there are 5 bacteria and we leave it for 15 minutes. bacteria will multiply to 10. if left for up to 30 minutes, 20 bacteria will form. if left up to 45 minutes. bacteria will multiply up to 40. every 15 minutes the bacteria will double 2. if you start with five bacteria that reproduce every 15 minutes, how manu bacteria would you have after 12 hours ?
calculate the product of 4 and 1/8
f(x)= 9-x^2 find (f(x+h)-f(x) )/h