1. Consider the following matrices A₁, A2, A3, B in the vector space M2,2 of 2 × 2 matrices, 1 -1 1 2 7 ^ = [ 2 ]] - 4 = [ †; } } ] - ^ = [ 3 ] = [¹/² 77²] A₁ A3 B 15/2 2 22 1 1 0 9 Express B as a linear combination of A1, A2, A3 if B € span{A₁, A2, A3}, otherwise show why B span{A1, A2, A3}.

Q: Find f(B)

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Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

A: This problem is related to the vector algebra. The problem is solved in the following image.

Q: A) find C= A.B for the following matrices 7 3] ;B B = 2 A = 24 3 1

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A: Given: The equations  06-1-1A+5-534B=4-60-2T0-211A+-4-8-3-6B=3-47-3T

Q: Use the matrix P to determine if the matrices A and A' are similar. -1 -1 - 13 6 6 6 P=[¯1 ¯2]·…

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Q: Construct a 3 by 3 matrix whose column space contains ( 1, 1, 0) and ( 1, 0, 1) but not (1, 1, 1).…

A: Column space: The set of columns of a matrix which are linearly independent is called the column…

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A: The rows of an orthogonal matrix forms an orthonormal basis. Therefore, consider the extended basis,

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A: NOTE: Refresh your page if you can't see any equations. . the given matrix is

Q: Find the matrices of the two similarities taking (0, 0, 1) to (-2, 4, 1) and taking (1, 0, 1) to (0,…

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Q: Find the inverse of the matrix 1 2 3 A-1) if A =| 2 3 1 3 1 2

A: Given,                  A=123231312

Q: X = 8 8 3 3 ; A = 2 42 0 1 -2 -3 7 3 3 2 9

A: Every matrix of order m×n is represented a linear transformation from Rn→Rm definition of T(x)=Ax

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Q: The symmetric matrix corresponding to the quadratic form X1 x2 = x} – 2x1x2 + 2x1x3 – 3x + 4x2x3 –…

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Q: find if the vector x is in the range for matrix A

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Q: Find a non-zero 2 x 2 matrix such that -5-2 6 15 -[88]- =

A: We have to find a non zero matrix such that the given rfelation satisfies.

Q: Let A and B be two n x n matrices. Call A and B simultaneously diagonalizable, if there is a single…

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Q: Factor these two matrices into A = XAX-¹: 4 = 3 A [

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Q: Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you know,…

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Q: Use the matrix P to determine if the matrices A and A' are similar. -1 -1 P=[11] 2 p-1 = 6 [2] 15…

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Q: Examplen' find the pvoduct of the follow ing (wo natricesi 2. 2. ら 1. 又3 3.

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Q: Let A be annxn matrix and B= A+T, where I is the identity matrix, then it is possible for A and B to…

A: Let λ be the eigen value of A. As B=A+I So, eigen value of B will be λ+1 which is not same as λ

Q: Find two unequal 2 x 2 matrices A and B such that 1 01 АВ

A: Given: AB=1001

Q: Show that (-A) T= -A", where A is a 2x3 type matrix (you can show it on the example)

A: Let matrix A=abcdef. Order of matrix A is 2×3. ⇒-A=-a-b-c-d-e-f ⇒(-A)T=-a-d-b-e-c-f  →Result 1

Q: 7. Let A = (; ) (a) Express A- as a product of elementary matrices. (b) Express A as a product of…

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Q: 3= b, ,b2} and C= (c,.c2} be bases for a vector space V, and suppose b, = - 6c, + 5c2 and b2 = - 4c,…

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Q: If the matrices A and B are conformable for sum A+B the product AB then prove that (A+B)" = A" +B"…

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