Construct a matrix whose column space contains (1, 1, 0) and (0, 1, 1) and whose nullspace contains (1, 0, 1) and (0, 0, 1).

Q: equations represented by the matrix shown [[5,1,3,37],[-1,1,1,1],[9,5,3,69]]

A: The system of equations represented by the matrix [[5,1,3,37],[-1,1,1,1],[9,5,3,69]] is           5x…

Q: 165 -0.31 |-165 -0.173 -0,517 Y EO -165 %3D

A:

Q: [4 -2] Let A be the matrix 1 Compute A50 1

A:

Q: Express as a single matrix.

A: 4  25-337

Q: Find f(B)

A:

Q: Suppose A is 17x17 matrix with A^29=0 Then A^17=0.

A: Here given that A is 17×17 matrix and A29=0.

Q: Put as many 1's as possible in a 4 by 8 reduced echelon matrix R so that the free columns are(a) 2,…

A: In a reduced echelon form of a matrix, if there is a pivot element in a row then, the elements above…

Q: find a matrix that column space is spanned by fewer vectors than there are columns in the matrix

A: The idea is the create a matrix such that one of the columns is in the linear span of the other two…

Q: Describe the column space of a reduced row echelon matrix R.

A: Leading 1: When the leftmost entry in a row is 1 and all the entries above and below of the leading…

Q: Given the matrix find A³. Write A³ as input your answer below: a11 a12 = a21 = 922 = = -[-3 0 A = A³…

A:

Q: ^T) + (B^T) and (AB)^T = (A^T)(B^T) if the orders of matrices are appropriate. * False

A:

Q: For the following matrix, A, A = 1 2 |3 1 1 1 1 1 2 1 | Q: What is the reduced row echelon form of A

A: To find Reduced row echelon form of the given matrix A

Q: |a b X y m nl

A:

Q: Let A be a diagonalizable 3x3 mat rix with P-AP=-I , where I is the identity mat rix. Which of the…

A: Let A be a diagonalizable 3x3 matrix with P^-1 AP = -I, where I is the identity matrix.

Q: [O 2 1 4 0 2 -2 5 1 [i 1 -1

A:

Q: Explain row vector in a 1 x n matrix?

A: To analyze row vector in a 1 × n matrix.

Q: Give a specific symmetric 3x3 matrix whose first row is [1 9 -2] 6. and whose second column is row…

A:

Q: (i) (3 3)-C ) - 6 3) y z 5

A:

Q: t A be the square matrix (abcd) A. If ad−bc = 1, then show that A^−1 =(d−b−ca ) B. If ad−bc=α, then…

A: If  is a square matrix then its inverse is where

Q: If the nulI snace of a 30x17 matrix is 13-dimensional, find the rank of the matrix.

A: We have been given the matrix which is of 30 x 17 i.e it has 30 rows and 17 columns. And it is also…

Q: Conotrut a onatn'x whode Columu 8pure (leli2) & whole cli5) 10 is spanned by now &pale in Bpanned by

A: Column space is spanned by 3-dimensional vector. Row space is spanned by 2-dimensional vector.…

Q: S)Give an example of a matrix A such that A2 = I but A#I or A± -I.

A: There are so many examples.

Q: Given A = 1 0 0 -3 1 1 1 - 2 -1 " x = and b = 300 150 400

A: Given that the system Ax=bHere A=1-3101-201-1 , b=300150400

Q: 1. A = 2. 0 2 1 4 1 -4 -1 -3 [1 B = 3 3 3 3 -3 97 10 10 -7 12 -1 9 -7 -6 2 2 2 -10

A:

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

A:

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x2 + 2y2 + 2z2-2xy-2xz- 2yz,…

A: We have to find the quadratic form of the equation Q=2x2+2y2+2z2-2xy-2xz-2yz which is a polynomial…

Q: If every row of a 4 by 4 matrix contains the numbers 0, 1, 2, 3 in some order, can the matrix be…

A: We can try to construct that. If every row of a 4 by 4 matrix contains the numbers 0, 1, 2, 3 in…

Q: Find the rank and the nullity of the matrix -2 -4 -2 -7 -1 -2 -2 -6 A 1 1 4 -1 -2 -1 rank(A)…

A: Given :-2-4-2-7-1-2-2-61214-1-2-1-4

Q: Solve the following system of linear equations using Row Reduction. (Set up an augmented matrix and…

A:

Q: evaluate the matrix

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

A:

Q: If A is a matrix that satisfies the following equation. Find: Trace(A-17I)^-1

A: Given,            A=pqrt-pq0082To find:  TraceA-17I-1

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

A:

Q: The equation A² - 2A + I = O implies that ---Select--- Need Help? Read It ✓. It follows that…

A:

Q: Rotate the quadratic function 5x^2 + 3y^2 + 2z^2 + 4xz = 14 to its principal axes and express this…

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Q: Write the 2X2 matrix associated to a reflection about the x axis.

A:

Q: -3 0 5] 1-3 0 5 18) 00 0 1 1 00 0 0 0 A) 5 B) 4 C) 3 D) 2

A: Consider the matrix

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.