Show that if A is both diagonalizable and invertible, then so is A-1.
Question:
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (10 reviews)
If A is diagonalizable then A PDP 1 for some invertible P and diag...View the full answer
Answered By
Pushpinder Singh
Currently, I am PhD scholar with Indian Statistical problem, working in applied statistics and real life data problems. I have done several projects in Statistics especially Time Series data analysis, Regression Techniques.
I am Master in Statistics from Indian Institute of Technology, Kanpur.
I have been teaching students for various University entrance exams and passing grades in Graduation and Post-Graduation.I have expertise in solving problems in Statistics for more than 2 years now.I am a subject expert in Statistics with Assignmentpedia.com.
4.40+
3+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Show that if A is nonsingular and diagonalizable, then A-1 is diagonalizable?
-
Show that if A is diagonalizable, with all eigenvalues less than 1 in magnitude, then Ak tends to the zero matrix as k .
-
(a) Show that if D is a diagonal matrix with nonnegative entries on the main diagonal, then there is a matrix S such that S2 = D. (b) Show that if A is a diagonalizable matrix with nonnegative...
-
1. Determine and confirm purchasing requirements for at least six (6) of the goods listed in the knowledge evidence. 2.Make purchase arrangements for the goods to meet different: End product...
-
Arthur Andersen Enterprise Group/National Small Business United, Washington, conducted a national survey of small-business owners to determine the challenges for growth for their businesses. The top...
-
Suppose that last month the U.S. dollar was trading on the foreign-exchange market at 0.85 euro per dollar, and today the U.S. dollar is trading at 0.88 euro per dollar. Explain what has hap pened....
-
The data given below show percentages of work completed for a construction project: Graph the data in Excel and comment on the shapes of the distributions. Forecast the cumulative percentages of...
-
A ventilation system has been designed for a large laboratory with a volume of 1100 m3. The volumetric flow rate of ventilation air is 700 m3/min at 22C and 1 atm. (The latter two values may also be...
-
1. Your client is charged with two counts of theft that relate to two separate incidents. At the first appearance, you receive a disclosure package from the Crown. Upon reviewing the material, you...
-
The following data were obtained from a study of the times required to conduct a consumer test panel study: Costs are given in thousands of dollars, time in weeks. (a) Find the all-normal schedule...
-
A is a 7 x 7 matrix with three eigenvalues. One eigenspace is two-dimensional, and one of the other eigenspaces is three-dimensional. Is it possible that A is not diagonalizable? Justify your answer.
-
Show that if A has n linearly independent eigenvectors, then so does AT.
-
Comparison of Alternatives Brian Imhoffs grandparents want to give him some money when he graduates from high school. They have offered Brian three choices as follows: a. Receive $15,000 immediately....
-
In this zone, we critically examine Fayols Five Elements of Management and consider whether they are still pertinent to organisations over a century after they were first proposed. Jules Henri Fayol...
-
Starting with (5.1.1) of the text, show that \[A=\frac{V_{\mathrm{S}} I_{\mathrm{S}}+V_{\mathrm{R}} I_{\mathrm{R}}}{V_{\mathrm{R}} I_{\mathrm{S}}+V_{\mathrm{S}} I_{\mathrm{R}}} \quad \text { and }...
-
Repeat Problem 5.43, but now vary the load reactive power, assuming the load real power is fixed at $1000 \mathrm{MW}$. Data From Problem 5.43:- Open PowerWorld Simulator case Example 5.4 and graph...
-
In this zone, we critically evaluate resistance to change and examine whether it positively or negatively influences the implementation and outcomes of organisational change programmes. Resistance to...
-
Joanne Mooney, customer journey and online experience manager, British Gas, based in Stockport, and her boss, Lucy Shadholt, head of channel development for British Gas New Energy, based in Staines....
-
Harris Company experiences the following cost behavior patterns each week: Fixed costs: supervisors salary $1,600; factory rent $4,000 Mixed costs: utilities $2,400 + $8.40 per unit Variable costs...
-
General Electric Capital, a division of General Electric, uses long-term debt extensively. In a recent year, GE Capital issued $11 billion in long-term debt to investors, then within days filed legal...
-
Determine which sets are bases for R 3 . Of the sets that are not bases, determine which ones are linearly independent and which ones span R 3 . Justify your answers. 1 -4 [F] 2 -5 -3 6
-
Find bases for the null spaces of the matrices given. Refer to the remarks that follow Example 3. Data from in Example 3 0-3 0 1 -5 3-2 2 4 1-2
-
Find an explicit description of Nul A by listing vectors that span the null space. 1 -2 A = 0 0 0 0 4 0 0 1-9 0001
-
1. A spotlight on a boat pictured below is 2.5 m above the water. A spotlight strikes the water at a point that is 8 meters behind the boat on the water's surface. The depth of the water is 4 m. How...
-
1. A high school athlete runs 1.00 x 102 m in 12.20 s. What is the velocity in m/s and km/h? 2. A person walks. 13 km in 2.0 h. What is the person's average velocity in km/h and m/s? 5. Suppose a car...
-
Suppose that a 0.225 m radius, 500 turn coil produces an average emf of 8800 V when rotated one-fourth of a revolution in 4.08 ms, starting from its plane being perpendicular to the magnetic field....
Study smarter with the SolutionInn App