Show that the rank of the linear mapping 7.32. Bar Y3= 301 +302 y = 201 +20203, 31-02-203 1 V2 is equal to 2 and determine the plane onto which E3 is mapped.

Q: The vertices of a rectangle are R(-5,-5), S(-1, -5), T(-1, 1) and U(-5, 1). After translation, R' is…

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Q: b) Use the idea in part (a) to determine an explicit one-to-one correspondence between zt and the…

A: as you asked only the solution for (b) , the solution of the part (b) is given below...

Q: In the projective plane, Z5P2, find the line that contains the points (1,2,1) and (2,1,4).

A: In projective geometry over a finite field, such as , we can find the line that contains two points…

Q: The determinant of the matrix -7 -5 A = -7 -2 -7 9. 0. -4 is and its inverse is [bu b12 b13 A= | b21…

A: Given matrix is A=−7−5−3−7−2−790−4. First find the determinant of A.…

Q: Prove that the equation 2x²+3xy - 2y-x+3y -1= 0 represents a pair of perpendicular lines.

A: Given that: 2x2+3xy-2y2-x+3y-1=0

Q: Do the points (0.5, 1), (1, 1.2), (2, 2) lie on a line?

A: Three points will lie on same line if slope of any two point is same as other two points, taken two…

Q: Determine the line of intersection between the following planes 12. 5x+2y-7= 9 and -2x+8y +9= = 3.

A: Given: The planes are 5x+2y-7z=9 and -2x+8y+9z=3 To find the line of intersection of the given…

Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: Find the equ. nf line through the Pont (-2,3,4) and Parallel to Planes: 2X+3y +42=5 3X + 4Y+52=6…

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Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

Q: iven the points A(2,6,0) and B(3,5,6) determine the point of intersection of this line to x-z plane.

A: Given points are A(2,6,0) and B(3,5,6) The line joining points (x1, y1, z1) and (x2, y2, z2) have…

Q: Find the value of X such that and are perpendicular

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Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: A company’s profit increased linearly from $6million at the end of year 1 to $14 million at the end…

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Q: Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

A: Given. A(x,5), B(2,3) and C(4,-5) are collinear.

Q: he intercepts of the plane given by

A: Intercepts of the plane are (3,5,3).

Q: P(−2,−3,6) is a given point and O is the origin. Find the coordinates of seven other points in three…

A: given: the point P(-2,-3,6) is a given point and O is the origin. we have to find the coordinates of…