5

4={824,,6,53 Qnd B= 27,9,41,0,10,83 let Gnd _ (a)(zb) Zab 122 i:2 (Lz < Lz I-2 62 62 0 315 04 64 2 + 4+/ : 7 (2)6) (vJlo) 6y-) 4t I + 0 2 41246 i:2 Qz b2- a3 6,+...

Question

4={824,,6,53 Qnd B= 27,9,41,0,10,83 let Gnd _ (a)(zb) Zab 122 i:2 (Lz < Lz I-2 62 62 0 315 04 64 2 + 4+/ : 7 (2)6) (vJlo) 6y-) 4t I + 0 2 41246 i:2 Qz b2- a3 6,+ G'y 64Z(,Yb,+1) i22 6,)l6z*i) = (Hli) _ (9,.,2(6,+1) . @) (12) Iz (64n) (6y4) 6)6)2f9) + (4?H0) + (2) 26 176 + 02i2

4={824,,6,53 Qnd B= 27,9,41,0,10,83 let Gnd _ (a)(zb) Zab 122 i:2 (Lz < Lz I-2 62 62 0 315 04 64 2 + 4+/ : 7 (2)6) (vJlo) 6y-) 4t I + 0 2 41 246 i:2 Qz b2- a3 6,+ G'y 64 Z(,Yb,+1) i22 6,)l6z*i) = (Hli) _ (9,.,2(6,+1) . @) (12) Iz (64n) (6y4) 6)6) 2f9) + (4?H0) + (2) 26 176 + 0 2i2



Answers

Exer $29-32$ : Find $A B$ $$A=\left[\begin{array}{rrrr} 2 & 1 & 0 & -3 \\ -7 & 0 & -2 & 4 \end{array}\right], \quad B=\left[\begin{array}{rrr} 4 & -2 & 0 \\ 1 & 1 & -2 \\ 0 & 0 & 5 \\ -3 & -1 & 0 \end{array}\right]$$

Consider that triangle uh, B and C. If this is the anger A then this part will be able to escape by two. Similarly if we draw like this, This will be be by two and this will be by to This is C x two and received by two and received by two. Okay then this will be say part then this be this eight, this is wide distance then we have Oh here this is 90 tickety, it's spy zack. This is our okay from this we have similar right by science by two equal to X by sign B by two equal to see by sign off 1 80 minus A plus B by two. It is huge. What name do you minus A Plus B x 2? That is equal to see by signing off A plus B by two And you got to see by Coz C by two That is equal to two are signs C x two. Similarly we can find why buy sign C by two Equal to set by sign B by two Equal to a bike owes a by two that is equal to two are signed by tooth, The full x equal to two are sign be by to sign C by two by equal to two are signs see by to sign a by two and set equal to our sign by two say B by two we got the values of expression for ex wife said now we can find the product X. Y said multiplying we get eight R. Q Signs Choir A by two Signs choir be by two Sign Square C x two. That is equal to one by two. Uh it's quite up this since Aries four are signed by two signed by two Sign C x two that is equal to two Window capital are square are signed by to sign B by two signs C by two Okay this is the first park now second but a plus B plus C equal to do this equal to assist to into delta by our that is equal to yes two Window to our Square sign a sign the sign see divided by whole divided by four are in new sign by to sign be by to science c by two smaller value this is equal to eight our calls a by two Cause be by two Go see by two on simplification we get light the sun no see pot X plus B, Y plus C six. This will be well due to our sign two Sign B x two Sign C x two place four are square signed by two sign the sign C by two plus four our Squire into signed A by to sign B by two sign see this will be equal to eight are square Sign me by to sign B by two Sign C x two. Common terms can be taken outset A two cozy by two Plus course B by two Plus go see by two. This is a mess to induce capital are in the smaller into course by two Plus calls B by two. Yeah. Plus course C by two. No option. The sub question the X, Y plus Y. Set plus set X equal to four. Capital are square. And you sign by two Side, B x two Signs Choir, C x two. Bless For our Squire. Sign a by two. Sign the way to into Science C by two and this can be rotunda's not is equal to fall our Squire Common terms signed a by to sign B by two Sci fi by two Common terms taken outside and inside the bracket we outside by two plus signed B by two plus Science C x two. A sequel to our into smaller into signing by two plus sign B by two Plus side. C x two. That's the ads.

Now here, in this problem, we are given matrix A. Is equal 2 1, 2, 3 456 789 And Matrix B is a matrix given by 100 010 001 And we want to find a B n B. A. Mhm. Now we have a very special matrix here. This matrix B is what is known as the identity matrix. The identity of any event. The identity matrix is a square matrix with one's along the diagonal is like we have here and zeros everywhere else. Something unique about the identity matrix is that if you take the matrix and multiply it by the identity matrix, it just stays the same. So even without doing any calculations here, eight times b is just gonna stay. And so it'll be 123 456 789 Similarly with B times A, it's just going to keep A the same. That's 1 2 3 456 789

So we want to sketch vectors and we have our initial point at the origin eso. The rest of it is really like plotting points A will have a negative three and then negative. 1234567 So once we do that, we have to draw a line because a vector is both direction and magnitude. And then we draw that arrow to signify that it's a vector. Then we'll have 123456 Negative, too. So that right there is going to be a vector of ours. That's B C will be zero negative eight. So we'll have 12345678 That's a vector that we're gonna have. Then we'll have 42 So 1234 up to the eyes and the jays correspond directly to X and y, respectively. Then negative, too. I negative j will go negative two in the extraction, negative one in the Y direction. So we see how this is very similar to X and y three. Only difference is drawing that line in the arrow to signify that's a vector has direction and magnitude, then four. I means that It's just for in the extraction, which is 1234 right here. So there will be no y direction. I'm just X, so that's our final vector.

In this question, we have to find whether the Given Victor's are equivalent or not. The first record that is Director D. J. Is given with the initial and terminal point as minus one comma one Goma and Jay is given video three comma one. So calculating the magnitude, we will get under root off to the minus off minus one. Holy square, bless. Run minus off minus one. Holy squared On further solving, we will get I know, dude off city Blessed one holy square. Bless one plus one Holy square. So this will give us under root off 16 Bless four. So this will come under root off 20 now calculating the magnitude off the second victor. Oh, if with the final on the initial point as zero comma zero and F is given video to come of one now calculating the magnitude of district er we will get under rude off within racket too minus zero Holy square plus one minus zero. Holy square. Now on further solving the under route, we will get I know dude off Dewey Square plus Vanni Square. And this will give us on the route off four plus one, which is equals to under root off five. So we can see here that the magnitude off BJ that that is not equals two magnitude off that O f. So the given vectors, Uh, not a curling.


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